Privatizing all roads would ironically probably be the fastest way to cut down on oversized vehicles. Nobody wants to pay a quadratic weighted toll on the GVWR of a bunch of extra SUV, but when they have to pay it all in taxes non-quadratically anyway it's a fuck it go big moment.
Let's see... If we privatize roads and every owner (pinky promise) only makes everyone pay basod on vehicle weight... That almost sounds like a tax based on car weight.
Some combination of both would be best in my opinion. Weight due to wear on roads and size due to the safety implications (some personal vehicles are now almost 2m tall and impossible to see over for pedestrians and cyclists - creating a much more dangerous environment).