The overall wheel weight does change performance. When I changed over to 125 lb LRH wheels from my 75 lb LRE's, I also upgraded to heavier dampened shocks to handle that unsprung weight better. I'm sure stopping and accelerating were slightly diminished with the extra rolling mass, but it was not noticeable. I think if I had changed tire diameter, it would have more affect.
I have a little on/off-road toy with only 20 hp and run a variety of wheel combinations based on terrain - This is a good test bed for experimentation since it is low powered and sensitive to changes. I run a 20" 2-ply paddle tire on 10" rims, 22" 4-ply trail on 10" rims, 25" 6-ply chevron tire on 12" rims and 25" automotive snow tire on a 14" rim. The automotive tire is the most efficient on roadways and almost as good as the trail tire until grades favor the shorter tire. The chevron tire takes the most power to run and is unusable in sand due its mass and height but has excellent traction and clearance. The sand tire is worthless anywhere but on sand and wears quickly but is short and light and lets the engine deal with soft material underfoot without bogging.
The point is that every tire/rim combination will excel at certain tasks and react poorly to others. If you want sports car handling, you will most likely not have weight capacity or traction as its strong points. If you want a soft compliant ride, handling and weight carrying will most likely not be that tire's best traits...