I think this idea needs more detail. How about this:
There are two traits given to each weapon: size and weight.
Now, for weight, strength is key. The character's ability to use the weapon would be controlled by the character's Strength, size, and number of hands available. Perhaps the "size" value is associated with a weight - say, 10s. Now, you multiply this weight by the strength number and the number of hands - such a character with strength 20 would be able to easily wield up to weight 200s with one hand, or up to weight 400s with two hands. Anything above this, and the character sees both to-hit and damage penalties. However, the PC would be able to wield one-handed weapons in two hands, or vice-versa, or in extra hands for that matter.
The second factor, size, would affect this in a different way - rather than being a factor that causes penalties for going too heavy, it instead limits usability. For instance, a troll would be rather unable to hold a small sword with two hands - it's just not feasible. A hurthling, on the other hand, would be unable to get the leverage necessary to handle a large mace without having more than two hands. These apply irrespective of strength, and are physical limitations that can only be overcome by dexterity.
Here's how I'd handle size: Character size as a number between 1 and 5 (1 being very small, 5 being very large). To this number, you add number of hands used, then subtract the item's size value. If the absolute value of the result is less than 2+(Dx/25), then the character can wield the weapon in that way. Note that this could probably be coded more efficiently as integers by multiplying everything by 25.
I would also add an extra case: one-handed weapons that such that the character size is larger than the weapon size. Such weapons would effectively act like extensions to hands, rather than full-fledged weapons. Consider the dagger - in real life, if you had one dagger, and was fighting, you wouldn't just use the dagger, you'd also use your other fist. However, if you had a sword, you likely wouldn't try to also use your fist - instead, you would use the extra hand to help stabilise when using the sword to block.
In this regard, I would make some "normal" weapons smaller than typical - normal daggers would actually only be size 1, for instance. Meanwhile, a typical quarterstaff would be size 5, making it a two-handed weapon for a normal-size character with typical starting dexterity.
Does all that make sense?