Simplify, simplify, simplify
My thoughts on how to fix weapons:
1. Stop trying to emulate physics. I have had more arguments at my table about weapon damage and effects than anything else. Why does a punching dagger have a lower crit range than a pick axe? Well, it's because the force of a pickaxe is more concentrated on the impact site because of the increased moment of intertia granted by the shaft of the weapon and blah blah BLAH. Who cares? Both are piercing weapons, so both should have the same crit range.
2. The stats of the weapon should be determined by its size and damage type. That's all. The name of the weapon can be chosen by the player or DM to fit the campaign, but the stats should remain fixed. A one-handed slashing weapon would be called a short sword, wakisashi, scimitar, khopesh, machete, or axe, depending on the setting. But they are all one-handed slashing weapons, so they all should deal 1d6 damage and crit at 19-20/x2. Every other difference is cosmetic.
This might be over-simplifying things. But I never understood why it had to be complicated in the first place.