Well probably you've never heard of issues because nobody cares to look into it. They throw huge wheels on their SUV or whatever and it just looks cool. And sorry i cant photoshop it to scale, or at all with those pictures you posted. I will be running 17/18" wheels, but with the 11 3/4" police brakes up front that were made to stop a mid 4000lb car..it should be no problem.
Rubber (tire) will weigh less than metal (rim).
If you keep the height if the wheel/tire combo about the same but increase the rim size from 15" to let's say 20", in theory the larger rim combo will be heavier due to there being more metal vs rubber.
When the combo is heavier, there's more "inertia".
Inertia = the resistance an object has to a change in its state of motion.
What that means is that it take more power to turn the wheels from a stand still.
When you have the larger rims you may get better handling though, but on autocross cars, you may see more "average size" rims and not 20"s because of the inertia issue and also you want "a little give" with the tires to compensate for over zealous driving. (Not that I know anything about autocross!)
I may be wrong on this stuff but it's just my
.