After doing extensive research and math on the possibilities of weapon damage based off the Power Up/Antidote Glitch and how it affects rollover damage (which happens after damage surpasses 255), I have been interested to make a few discoveries. (TL:DR at the bottom)
-Any%- Weapon Choices in Any% is actually a bit easier to make as you only have really two shops to choose from and only two characters to worry about: Nei and Amy. This limits you to really only 5 weapons to choose from: Steel Bar, Ceramic Bar, Knife, Scalpel, and Ceramic Knife (though you could grab a Fire Staff in the Red Dam, but more on that later).
The currently accepted method for Any% routing involves 2 Ceramic Knives for Amy and 2 Ceramic Bars for Nei. Since encounters are minimized as well by the numerous glitches, choosing your weapons basically comes down to what will do how much damage to Dark Force and Mother Brain.
First with Nei's weapons. The Ceramic Bar on average will deal about 105 Damage to Dark Force and 220 Damage to Mother Brain (rollovers factored in). The Steel Bar, on the other hand, will deal 191 Damage to Dark Force but only 68 Damage to Mother Brain (again, rollovers factored in). To get max damage in both fights, it would be required to switch weapons after the Dark Force fight (382 per round for Steel Bars on Dark Force and 440 per round for Ceramic Bars on Mother Brain), but switching would take up menu time which can be the difference between a PB or not.
So let's break this down. If Nei were fighting alone, it would take nearly 7 turns to down Dark Force (providing each attack hit) with Steel Bars and 12 turns with Ceramic Bars. However, if you equip one of each for this fight, it would only increase the amount of turns needed by 1-2 for Dark Force. Likewise, against Mother Brain, 2 Steel Bars would take 17 turns while 2 Ceramic Bars would take about 6, but one of each would raise it to about 8-9 turns.
So in the end it all comes down to one thing: How fast can you menu and how much time would it take you to buy one or two Steel Bars at the beginning? If you can go through menus fast enough, having a set of Steel Bars and Ceramic Bars for the final two fights (or one of each if you can pull off an Equipment Glitch fast enough) will probably net you with faster times and quicker kills with the final two bosses. If you feel slow on the menuing, having one of each equipped at all times will result in greater consistency. As far as the time it takes to buy the Steel Bar(s), consider that having at least one steel bar will cut off at least 2 turns off of Dark Force alone (4 turns if Nei is alone, but since she is not, using a 1/2 estimate). The time spent at the shop in Paseo to get this weapon is generally less than 2 turns in a battle, but keep in mind that Dark Force can still be a troll).
As for Amy's weapons, given the options, the Ceramic Knife deals the most damage to both Dark Force (211 per hit) and Mother Brain (167 per hit) providing you buffed her with Antidotes (which is recommended). A Knife and Fire Staff on average will deal more damage to monsters on your way to the final bosses, but that isn't a big deal in Any% when you only really have to worry about Skure and Dezo enemies. It is an added bonus that you need two Ceramic Knives in order to get 3 of the Nei Items. The Fire Staff will do the SAME amount of damage to Dark Force on average, but LESS damage to Mother Brain, so it makes 2 Ceramic Knives truly the only viable weapon in an Any% run.
If you are wondering about weapons for Rolf and Rudo, equipping anything on Rolf won't even break 50 damage on either boss and will only serve to eat up precious time. The Nei Shot on Rudo can deal about 100 damage, but against Dark Force, he won't last long anyway and there would be no sense to revive him for Mother Brain since she will 1-2 shot him anyway. So just leave them be as a damage soak/curse beacon for Dark Force and let the men just die. Don't bother equipping them with anything.
-100%- This is where weapon choices get interesting as you have to worry about enemies all across the game. Because of this, Anna is highly recommended with her Slashers to clear out mobs fast. But we will get to that in a moment.
Choosing the right weapon here means you have to take into consideration how likely a weapon is to kill an enemy in one or two hits AND which item you use to buff your characters (Antidote is generally the best rule of thumb and was used in the calculations. If I find better results I will post them). After tons of math and research into enemy HP, Defense, and how the overflow affects the damage formula, I developed what is known as a Heat Index for weapons. In sense, it is like this: If a weapon would take more than 2 hits to kill an enemy, I labeled it as a cold weapon against that enemy. If the weapon can one or two shot an enemy, I labeled it as hot. The more weapons that were labeled as hot, the higher number it would have on the Heat Index. (at some point, I will load my charts to a pastebin or something similar once I fine tune my findings).
I also discovered that because one weapon can be hot against an enemy while another cold against the same enemy, I found it generally a good rule of thumb to never equip two of the same weapon unless you are in a boss fight.
So let's start with Nei, who only has 3 choices to begin with. The Steel Bar actually has a higher Heat Index rating than a Ceramic Bar and does more damage to Nei First as well. That being said, the Laser Bar (which can be bought in Kueri) has a higher Heat Index than either of them and does twice as much damage to Nei First than the Steel Bar. Thankfully, as well, most the monsters that the Laser Bar is cold against will NOT be seen by Nei (only Spit Kill and Toader from my calculations would take minimal damage from it), so dual wielding Laser Bars once you get to Kueri would theoretically maximize Nei's damage.
Now let's look at Anna. She actually uses the weapon with the highest Heat Index which is the Boomerang. Unfortunately, the Boomerang is a single-target item, unlike the other slashers, and the throw animation is longer than melee weapons, making the Boomerang a bad pick in a speedrun. That leaves the Slasher, Laser Slasher, Fire Slasher, and Nei Slasher (The AC Slasher is never obtained in the run and in fact is rather weak on the Heat Index, so that weapon is omitted). The Slasher and Fire Slasher are both equal on the heat Index, but the Slasher has what I like to call a higher "Kill Factor", or the ability to one-shot an enemy. Though I used the Fire Slasher in my WR run, in future attempts I will be omitting this item as the item's damage is too close to that of the Laser Slasher, so the enemies it will be cold against will be similar (again, going with two different items in each hand to minimize the chances of battles going over one turn). The Laser Slasher is actually a very good weapon with a high Heat Index and even has a slightly higher index than the Nei Slasher. However, the Nei Slasher is cold against a lot of enemies in Dezo, including Dark Force (though it performs very strongly against Mother Brain at 214 damage per hit). Both the Slasher and Laser Slasher deal moderate damage to Dark Force (148 and 168 respectively) and the Slasher deals similar damage to Mother Brain. However, the Laser Slasher deals AMAZING damage to Mother Brain, BUT, it is to a point where it might be too amazing (242 damage on an average variable roll in the damage formula). This could be risky if Anna got higher strength gains in her initial level ups after Powering her up and/or she gets high variable rolls, and since there is no way to really tell what damage is being done to the final bosses, using the Laser Slasher against Mother Brain could net in a DPS loss (but then again, it might not).
So for Anna, using a Slasher and Laser Slasher through most of the game should net in the most balanced DPS with dual-wielding Laser Slashers for the final two bosses. If you feel worried about a potential overflow against Mother Brain, you could go with a Slasher and Nei Slasher.
That leaves everybody else now (Rudo, Amy, Hugh, Kain, and Shir). Rudo, Kain, and Shir can use Daggers, Amy and Hugh can use Scalpels (which deal the same damage as Nei's Steel Bars), Amy can use a Fire Staff, Anna can use a Whip (which does the same damage as Ceramic Knives), Hugh and Kain can use Laconian Maces, and Shir can use a Laconian Dagger. Surprisingly, both Laconian Maces and Daggers performed VERY well on the Heat Index, but since there is no easy way to obtain them (because we do no shopping in Dezo and I have not found an easy way to get them through an Inventory Glitch yet), those items are being omitted. Also being omitted are shots and guns, as their damage calculation does not factor in the massive attack gains from the Antidote Glitch, so there would be no benefit to using them).
A Knife has a high heat Index but performs poorly against Mother Brain (53 damage per hit) and average against Dark Force (148 per hit). The Ceramic Knife performs well against Dark Force and decent against Mother Brain, which the Laser Knife (bought in Zema) is slightly weaker against Dark Force (126 damage) but is the strongest weapon against Mother Brain outside of the Laser Slasher (227 damage). The Heat Indexes of the Ceramic and Laser Knives are also similar, and on average where one weapon is cold to an enemy, the other would be strong against.
The Scalpel, Dagger, and Fire Staff are all good weapons with high Heat Indexes as well (though the Scalpel is a bit weaker in that regard) and all deal great damage to Dark Force (each hovering around or above 200 damage), but they are all VERY weak against Mother Brain. Because of this, for the remaining 5 characters, it is recommended that having a Ceramic Knife and Laser Knife would optimize consistency and damage.
Remember what I said about not having two of the same item equipped at the same time while going through to minimize odds of a cold item (this includes two different characters as well)? It may be feasible to keep at least a Scalpel and Dagger wielder around at the same time (for instance, Amy with a Scalpel and Laser Knife, Shir with a Dagger and Ceramic Knife). You could play around with it potentially, but until further testing is done, a Laser Knife and Ceramic Knife makes for the best combination.
THIS being said, much like the Any% fights, if your menuing is fast enough, you could use 2 Ceramic Knives for the Dark Force fight and 2 Laser Knives against Mother Brain. This also includes having Anna equipped in that manner as well for the faster animation speed.
-Conclusion- Thanks to Jiseed's Antidote Glitch and the discovery of damage overflow, a need for figuring out what works best can be quite a daunting challenge. I hope this post/guide provided some insight. Keep in mind that these calculations were done on averages and on what the possible max Attack Power a character gets could be. Your results may vary slightly from my findings and math.
-TL:DR- Any% Weapons: Nei: 2 Steel Bars for DF, 2 Ceramic Bars for MB, or one of each if your menuing is on the slower end. Amy: 2 Ceramic Knives, no questions.
100% Weapons: Nei: 2 Steel Bars up to Kueri, then 2 Laser Bars Anna: 1 Slasher and 1 Laser Slasher, then 2 Laser Slashers against DF and MB (or Ceramic/Laser Knives if your menuing is fast enough). Everyone Else: 1 Ceramic Knife, 1 Laser Knife (can switch to 2 Ceramic Knives vs. DF and 2 Laser Knives vs. MB if you can menu well).
Places to buy Weapons: Steel Bar: Paseo Ceramic Bar: Oputa Laser Bar: Kueri & Piata Slasher: Zema Laser Slasher: Kueri Ceramic Knife: Arima & Oputa Laser Knife: Zema
The research paid off in dividends, as I knocked 16+ minutes off my WR for 100%, down to 2:27:39. I used the item recommendations for the MOST part (I left a dagger on Shir with a Ceramic Knife up until Noah). I was going to leave Amy with a Scalpel for the "No Duplicate Items" rule, but I accidentally tossed her Scalpel. Lol.
Nei wrecks through Neifirst with 2 Laser Bars. This setup is optimal.
Using Amy and Shir with a Ceramic Knife and Laser Knife each, as well as Anna with a Slasher and Laser Slasher, both Dark Force and Mother Brain fights lasted under a minute (56 seconds for Dark Force and 39 seconds for Mother Brain). I don't believe that taking time to menu will to switch to double Ceramic/Laser will be beneficial, as the time taken to switch versus the time saved in the fight would be very minimal at best (you may end up losing time in the process). I believe this setup in the endgame to be optimal.
What is even more surprising from my run... Rolf didn't die during either Dark Force or Mother Brain fights.
I will try to upload the video at the end, but because OBS disconnected about 2 hours in, the video ended up being split with a bit cut out. I have them on youtube, but I doubt anyone will confirm it on here as new WR for the site.