This post is primarily related to the ability to grasp large weapons with a single hand, but it also has implications for multi-grasping large weapons by small creatures...
All melee weapons are a lever, and most attacks utilize this, swings in particular. To move a lever you need 2 points of contact, a point where you apply pressure, and a fulcrum. There are actually multiple levers at work when swinging a sword, your hand makes two points of contact to hold the sword steady, and your point of rotation, such as your shoulder, makes a fulcrum for a larger leaver encompassed by the sword and your arms. For both levers there are 2 points of contact.
This is why some weapons are simply two handed in real life, you need to space those points of contact out to maintain control. When you are holding a sword, part of your hand is a fulcrum, and another applies a force to counteract the torque made by the fulcrum and gravity. Larger weapons have a greater torque, and because its a lever you can counter that force by spacing out the fulcrum and where your hand applies pressure.
This creates a real upper bound on how large a weapon you can wield and strength only helps so much. Its true that, if there is no limit to the force you can apply, then the distance between your fulcrum and that force can be as small as you like, but there are very real limits to that force you can apply, and it only varies slightly with increases in strength. Therefore some weapons must be wielded with 2 hands in real life (even if it can be held in certain positions with a single hand, control will be minimal and movement will be limited).
The same will scale down to dwarves, smaller hands mean smaller weapons for single-grasp. Smaller arms mean smaller weapons for multi-grasp. Though the issue is easy to scale for what weapons must be multi-grasped, its more difficult to see how it should scale for weapons that can't be grasped at all.
I agree strength should be a part of the role, but not the determining factor. In fact, I agree here size is certainly the determining factor, strength's role would be quite minimal and maybe even negligible in my opinion. I think the weight of the material has much more to do than the strength of the wielder, as such:
Seems like an adamantine anything would be light enough to swing around no matter what. With the incredible sharpness, the wielder wouldn't even need any force behind the weapon.
I agree.
TL;DR: Melee weapons are a set of levers, and the space between the fulcrum and your point of force makes a much greater difference than the amount of force a stronger person can apply. Size really is more important.