Maybe I'm still not getting it, but let me throw some things out there. Hopefully some others with more Newtonian Mechanics than I will chime in and shed some light. This looks like this could be a multi-faceted Mechanics problem, although I'm still having trouble understanding the exact problem.
1. I see the rotating wheel having rotational inertia
2. I see the "same" rolling wheel having inertia in the direction of travel
3. The first sentence asks "How is rotational inertia effected by weight if at all?"
Ill assume the "load" placed on these wheels is like the body of a car, or the body of a motorcyle, 4 or two wheels respectively. This coupling, or connecting to the wheels changes many things from a Classical Mechanics perspective.
If the car body was nearly zero in mass, and the car traveling in a straight line, I think the "coupled",(two or more wheels tied together), rotational inertia would be minimally effected.
If the car body was large in mass, the wheels rotational inertia would have only a small effect on the vehicle.
There are many variables possible in your question. I believe the answer could vary wildly given the adjustment of certain variables.
4. "mass of the load should be incorperated into the inertia at all" I'm scratching my head with this statement. Is it saying to alter the wheel's inertia,(by changing wheel design), if the cars mass has a significant influence?
5. What is the "goal" of the wheel design? , performance? gas miledge for a given mass?
Maybe I'm over analyzing the problem, hopefully I have been some help, perhaps someone will shed some light on this problem for both of us.
