With all the weapon complexity in the game, I find the weapon damage rules from the Dungeon World RPG to be refreshing: All characters deal damage based on their character class, regardless of what weapon they're using.
So, a Fighter always does 1d10 damage, whether he's using a bow, or a sword, or a polearm, or a dagger.
A Wizard can use a sword in combat if she wants, but she'll only do 1d4 damage... same as a staff or a dagger.
This eliminates the need to calculate what weapon is best for your character options, and completely opens up everything for your character's style.
13th Age has a a similar system, but makes a few distinctions, such as between one handed and two handed, or martial vs simple. Some classes suffer a penalty if they try and use certain weapons. The system also simplifies armor in to light, heavy, and with shield for each class. Again with certain classes suffering a penalty if they try to use something to complex.
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I've done something to the 13th age system, where the damage you do is determined by your class, the type of weapon you're using, and the subtype of weapon you're using.
So a fighter using a generic two-handed weapon would do 2d6, but a fighter using a reach two-handed weapon would use 1d10. Describe these however you like. A fighter using a 1 handed weapon would do 1d8, but a fighter using a finesseable 1 handed weapon would do 1d6.
You have to figure out how you would work in things like brace, trip, disarm, etc. but you could easily let people add those for a cost like weapon mods. There's a number of different ways to go with crit range though.
I'm sure you could come up with a points based system with perks like a better crit range or the disarm ability. It could be basically a more flexible version of the existing Pathfinder system, or the GM could just allow any combination of weapon qualities which seems "balanced" without worrying too much about the exact name. For instance, a Martial one-handed weapon which can trip and disarm and does 1d8 damage seems reasonable. If it had 19-20 crit range too maybe it should only do 1d6 damage or be Exotic.
Another option could be a more narrative system where you can claim bonuses (+2 on this or that) by describing how your weapon helps you achieve the goal (a chain for disarming or tripping, a shield for bull rushing, etc)
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You want more simplification? You kids don't know how easy you have it, no weapon speed factors, damage not changing against large opponents, and you've never seen the horror of the weapon attack adjustment vs AC table.
Now get off my lawn.
-The preceeding brought to you by 'Codgers Who've Been Playing This Game Way Too Long, Inc.'
@GM Rednal - Sure, like I said, somebody could come up with a points based system. To me using that sort of system seems like more work than just looking at the existing lists, but it could be nice if somebody wants a very specific weapon or capability and the GM doesn't want to make a judgment call on what seems "fair".
You want more simplification? You kids don't know how easy you have it, no weapon speed factors, damage not changing against large opponents, and you've never seen the horror of the weapon attack adjustment vs AC table.
Now get off my lawn.
-The preceeding brought to you by 'Codgers Who've Been Playing This Game Way Too Long, Inc.'
+ 10 LOL! Damn kids!