By and large we already do that. The larger vehicles are more expensive, and in most states your tabs are based on the price of the vehicle. If you want to go a step beyond that, I'm sure you'd be able to find some support if it wasn't an outrageous tax. This assumption that because OP doesn't need a large vehicle, nobody has a reason to need one is just silly.

And as I said, it does absolutely nothing to address parking lots.