Just to throw another mechanic into the mix...
I always think that the immersion is lost a bit in games where you reach level 100 in sword, and then decide that you want a bit of a change and pick up a mace, only to find that you're level 1 and swing it like a pixie.
Aragorn is awesome with a sword... but he's hardly going to crumble with an axe/mace/dagger in his hand, is he?!
Basically, I vote for a 'stackable' weapon prowess system, that at a very abstract level works like this:
(1) Individual weapon prowess. E.g. for sword, axe, bow, shield, or fist. Represents real mastery with a weapon of choice - each weapon class has it's own prowess level, and this governs (or unlocks) special moves and abilities with that weapon.
(2) General melee weapons prowess skill level, which generally improves skill of everything used in hand-to-hand combat. Represents general skill as a fighter. This is upgraded whenever ANY individual weapon skill level is upgraded. Or perhaps it would be better to base it only on the highest (or highest two/three) individual weapon skill levels, so that you don't get caught into grinding through all of the possible weapon types just to increase your general weapons prowess.
(3) General ranged weapons prowess skill level. Exactly the same as the melee weapons prowess level, but for ranged weapons... just because you're good with a sword doesn't mean you can aim a bow, and vice versa.
Mechanics for special cases, like dual-wielding (which e.g. includes sword-sword, sword-shield, sword-axe) would have to be thought about carefully.
To complement such a system, Bare Mettle have already said that suitability for characters to be naturally more suited to lighter or heavier weapons will be implicitly based on their body type, and governed by physics. This is fantastic! Can't wait!