A fully loaded semi is 18,000 lbs per axle. A really huge personal vehicle, an F-350, is 4000 lbs per axle. That's 4.5x the weight, 4.5^4=410, so the semi is doing 410x as much damage. There's really no point in trying to tax personal vehicles for road damage when over 99% of the damage is being done by trucks.
Even driven at gross weight, it's doing 5% of the damage per axle of loaded semi. The semi also has 4-5 axles, so it's more like 2% of the damage of the semi.
Mind you, we're talking here about the most damaging personal vehicle loaded to its maximum weight, and the semi is still doing 50x the damage of the personal vehicle. It's reasonable to say that essentially all road damage is done by semis.
That said, this type of tire is a very tiny fraction of the total miles driven on public highways, and so if you're looking for someone to tax based on the costs they create, it's all heavy trucks.
Trucks and permit loads are pretty much the only things that get close.
Beyond the elastic limit, damage is an exponential function of the pavement loading, but only once that certain minimum psf is hit.
For the majority of a highway's loading curve, the damage-per-force is essentially nil. Plastic deformation and serious fatigue only start as you approach the design limits.
It's 99%+ because cars don't do any real wear or damage to pavement from typical use.