This would require dividing weapons into simple categories, like One-Handed and Two-Handed, with a short description of each -- enough to easily determine how the aspect can be used. If you're wielding a dagger against a guy using a two-handed sword, you could invoke your "Dagger" aspect in pursuit of getting in close enough to render his big sword ineffective.
(BTW, I'd probably call it Melee limited by Athletics, since you're trying to twist your way to corps-à-corps and attack -- it just feels right to me. YMMV. I could also see doing that bit as a maneuver to place a "Corps-à-Corps" aspect on him, which you could tag next round to help your dagger attack, or just make it a straight Melee roll and say that the maneuvering is just part of the attack. All make sense to me. I think I like the first one the best, but going the maneuver route makes it nice and tactical.)
Then, when he tries to attack you, you could tag his weapon's "Greatsword" aspect to add to your defense.
The point is this: We know what these weapons do, so I'm not sure they also need aspects to tell us the same thing, again. It's a longsword -- a three-foot piece of steel for stabbing and slashing. It's a battleaxe -- big choppy thing. It's a longbow -- its arrows can pierce plate. And so on.
The "stat block" for armor currently looks something like this:
Armor: Medium (Good +3)
Aspect: Chain hauberk
Consequences: +1 Minor/Moderate
So why not have weapons look like this?
Weapon: One-Handed (+1)The name of the weapon itself actually has a mechanical effect without the need for any other subsystems or anything. You have a pike -- pikes are long by definition -- you can take advantage of that to keep someone else at bay -- that translates to being able to invoke the "Pike" aspect to add to your defense against an incoming attack. If that attack lands, and your opponent is using, say, a longsword, then he must've gotten close enough that the effectiveness of your pike is reduced -- so now you can't invoke that aspect to attack or defend, but he can tag it to add to his own attack and defense.
Weapon: Light One-Handed (+0)
Special: No effect if target is wearing armor
Weapon: Missile (+1)
Aspect: Short Bow
Special: 2 zones
Weapon: Heavy Missile (+2)
Aspect: Long Bow
Special: 3 zones
Weapon: Two-Handed (+2)
Weapon: Heavy Two-Handed (+3)
Aspect: Troll Axe
Special: When dealing a consequence, spend a Fate Point to also place a fragile aspect on the target.
Of course, you need a few addenda for this to really work. One, as mentioned above, is a brief description of each weapon that makes it abilities and limitations clear, with sample invokes, compels, and tags -- at least one of each -- to make them even clearer. Two is categories with pre-determined attack modifiers. That's more or less what I did already; this would just be codifying it. For example, Light One-Handed weapons are +0, One-Handed are +1, Missile are +1, Heavy Missile are +2, Two-Handed are +2, Heavy Two-Handed are +2 with the aspect-placing ability mentioned in the Troll Axe writeup above, etc. Three, you need... er... well, that might be it, actually.
I think this has some merit. I'm all for simplifying things without losing depth.