Yes, you really do want to. It would be lovely if we could charge proportional to the externalities.
As for how... beats me. Best we can do is rough approximation, and accept that we will continually find out we were wrong and have to adjust the cost structure.
We could get the approximations quite wrong and still get massive economic improvements from where we currently are!
However the challenge isn't the approximations, but the political difficulties. Even taxing based on mileage would cause an uproar. And taxing large pickups proportional to their economic toll on infrastructure would probably start a violent revolution.
There are a lot of smaller roads where 18 wheelers never travel, and where a 2x weight increase means 10x the road wear (between the cube and fourth power of weight, according to simple models in this thread).
The how is difficult -- studies like this are part. "Do you really want to?" is a clear yes. It's called a Pigovian tax, and it's the most unambiguously "correct" way to tax things: you tax things in accordance to their harm to third-parties (and subsidize things in accordance to their benefits to third-parties).
Markets only work if we internalize the externalities, which can most efficiently be done through taxation. Pollution is one of the standard examples of an externality.
Charge the asphalt companies a carbon tax, and let municipalities create road taxes based on vehicle weight/usage to pay for the extra costs created for road maintenance
In other words, how do you price in the pollution? And do you really want to?