What taxing by weight would do is not encourage people to "make the right decision" but punish people who need to have the heavier vehicle. It already costs more to run most of those heavy vehicles, so most people don't own them unless they need them or can afford the extra cost. In the first case, those would be people who farm, tow heavy stuff, do construction work, etc. In the second, a sin tax on a vehicle would not matter. They can afford the cost.
My state already tried this with recreational vehicles. Not that they wanted them off the road, but they saw another source of revenue by increasing the tag tax. People who could afford the vehicles in the first place paid the extra and there were no fewer rec vehicles on the road.
since we can usually find examples of things already tried, it's a good idea to look for those first and figure out if they were effective and who was really hurt or helped by the change.
