This is what I have right now:
Weapons are broken into three broad categories: Basic, Simple, and Martial. Note than any given weapon type may represent quite a few different actual weapons, depending on the milleu. A one-handed single-edged blade could be a machete (cutting through tropical jungles), a German messer (pseudo-medieval Europe), or a Scimitar (psuedo-Arabian Nights).
Clubs & Staves (Lt Club, 1H Staff, 2H Quarterstaff)
Single Edged Blades (Lt Daggers)
Slings (Lt Slingshot, 1H Sling, 2H Staff-Sling) - Maybe
Unarmed (1H Pummeling)
Maces (Lt Horseman's Mace, 1H Footman's Mace, 2H Heavy Mace)
Single Edged Blades (1H Machete/Scimitar/Messer, 2H Voulge/Bill/Glaive/Bardiche)
Spears (Lt Short Spear/Dart, 1H Spear/Javelin, 2H Longspear/Pilum)
Crossbows (1H Crossbow, 2H Arbalest)
Unarmed (Lt Sparring, 2H Boxing)
Hammers (Lt Throwing Hammer, 1H War Hammer, 2H Maul)
Flails (Lt Horseman's Flail, 1H Footman's Flail, 2H Dire Flail)
Swords (Lt Short Sword, 1H Long Sword, 2H Great Sword)
Axes (Lt Throwing Axe, 1H Battle Axe, 2H Danish Axe)
Picks (Lt Horseman's Pick, 1H Footman's Pick, 2H Bec-De-Corbin)
Bows (Lt Shortbow, 1H Longbow) - Requires 2H, just falls into those categories for interactions with other rules
OTHER MARTIAL WEAPONS
I'm thinking about eliminating or simplifying these altogether.
Lances (1H Lance, 2H Heavy Lance) - Requires 2H mounted, considering eliminating this category and rolling it into spears
Advanced Polearms (1H Trident/Military Fork, 2H Halberd, 2H Ranseur, 2H Guisarme, 2H Pike/Partisan)
Unusual Weapons (Grab bag of misc setting specific type stuff; Sabers, hand crossbows, whips, saps, etc)
Now for the interaction with ability scores. Ready? Buckle up. You gain different proficiences based on your PRIME ability scores (you have two, remember?). You gain the benefits of whichever are LEAST restrictive.
STR = All melee and hurled weapons (basic, simple, martial)
DEX = Basic only (gain bonus with light weapons)
CHA = Basic & Simple
CON = All weapons (basic, simple, martial; melee and projectile)
INT = Basic
WIS = Simple
Above is the interaction of these proficiencies. As you might expect, Wizards are highly limited. Fighting-men can use anything, although Swashbucklers tend towards light weapons. The main non-warrior melee characters, Eldritch Knights and Paladins, can swing swords or hammers or axes around, but they don't get bows. Archery is the exclusive province of the Fighting Man. Priests can use their traditional maces as well as spears and single edged blades, which makes building a Shaman-type quite viable, broadening the archetype some without shattering it.
This also nicely cements the place of the Crossbow as the everyman's projectile weapon. Everyone except for Wizards and Eldritch Knights can use Crossbows.
I think the number of choices will be quite reasonable. The most complicated case is the Warrior. He has five martial melee weapon choices to select from and enough STR to have a high ENC limit. He also can pick up one of several projectile weapons. After he's decided what family of weapons to obtain, he needs to select from a light, one handed, or two handed variant. So, we're looking at a three step decision process: Melee or Projectile, Family, Type. No step has more than 5 choices.
The other class archetypes have even fewer choices. I think there are enough to keep things interesting (especially once you give defining characteristics to the weapons themselves) but not so many options that players are overwhelmed or feel it difficult to make choices.