The katar should definitely have a stab contact area similiar to a dagger since it was primarily a piercing weapon by design so that looks good. They were designed to punch through armor. You've made it bit heavier and longer than a dagger which also fits it well. The blunt attack seems a bit out of place on a weapon like this. This is one weapon where I think it could really do without a blunt attack.
The rock hammer/pick looks good except for the extremely deep penetration. It's penetration should be more like 3,000 or 4,000.
The ice axe also looks good except for the crazy high penetration. It should also be lowered down to maybe 3,000 or 4000. 10,000 is the sort of penetration you see on a piercing pole arm.
You will find that the quarter staff does not perform well at all with those stats. It also doesn't need those super high penetration values nor do they make much sense on a staff.
To make the staff a viable weapon I would increase it's size to 600. Decrease its contact area considerably and give it a high velocity multiplier since you get a good bit of leverage and speed with such a long swing. I think a contact area of around 200 and a velocity multiplier of 3000 would make for a good bash attack for the staff. A blunt jab with a contact area of like 20 and a lower velocity multiplier of like 1000 would make a reasonable second attack type. Penetration of like a 1000 sounds fine for both attacks.
The way staffs are generally used, its pretty much a two handed only weapon. If you go so far as to simulate that by giving it an impossibly high one handed wielding value then you will probably want to buff it further by giving it a fast recovery speed to make up for the massive penalty of having no shield with it. It also fits well with how the weapon is wielded in real life as staffs can strike alternately with each end without having to wait for the back swing.
The flayer looks just like a scourge to me minus maybe the slower attack speed? I can't remember if scourges got the same treatment as the whip in the new version or not. Either way it looks fine. Not a super powerful weapon by any means but it fits well with its design.
As for the bow I'm not familiar with them in this version. I know Toady MASSIVELY nerfed them so arrows impact with a tiny fraction of the energy they used to. If your short bow is based off of how bows used to be then it will be many times more powerful than its counterparts in DF2014. If you want to make it kind of different give it a 2:2 recover time and make it weaker than a standard bow.
Were you aiming more for realism or balance with these weapons?
Balance, 100%
Katar has a backhand attack because all of the blades have "flat slaps", with a large knuckle blade I imagine just the person backhanding someone to do a blunt attack.
Pickhammer nerf I can agree with.
Ice Axe nerf I can agree with.
Quarter Staff penetration is weird, it shouldn't actually have any (the wiki shows negatives on maces and such, but the files don't have negative values, I was really confused on if it automatically assumed Blunt was negative) I would like to force two-hand, and would like a lot of just straight bashing with a lot of attacks without making it a knockout instantly kinda thing. Faster swing speed definitely sounds like what I'm wanting to do (as well as value shifts.)
Flayer is just a Scourge by a different name, I wanted to implement custom weapons without having to worry about editing vanilla stuff later for balance or changes.
Shortbow I /might/ have used the old bow values, I probably need to shift them. I think I'm going to nerf its force a lot compared to a normal bow but make it fire faster, then the Long Bow would be the opposite.