Why preserve the opacity of that relationship? Tax trucks higher, and it will reflect in the prices of the products those trucks are hauling, fairly distributing the cost increase of their operation across the consumers of those products.
We absolutely should tax goods and services based on the negative externalities they impose. Taxing vehicles by weight is a fair tax, much more fair than doing the _exact_ opposite right now, work trucks being taxed less. Heavy vehicles used productively will remain, but spending on heavy vehicles for recreation will be less attractive, since that kind of use consumers balance against other discriminatory spending.