Unsprung weight will effect handling as said above, it is only dampened by the tyre other than that its free to bounce about. Imagine driving a car with no dampers.

There is no proportion between sprung and unsprung mass in terms of handling, totally dependant on the car, damper etc.

What will effect the effective weight is rotating mass.

This is because you have to make it accelerate in 2 direction (forwards and around).

That is all to do with inertia so again it is not just the weight but the shape of the object.