can't remember the exact equation but I recall that damage done to the road surface is proportional to the square or cube of the vehicle mass - hence why cycle lanes essentially never need to be re-surfaced.
The damage done to the road surface by each axle is proportional to the
fourth power of axle load. You then need to sum across the number of axles. And to be fair, also multiply by the mileage driven.
Incidentally, the same law ought to apply to rail vehicles, illustrating why keeping axle load down keeps the permanent way people happy.
Just based on weight and average mileage, I worked out a while ago that under such a system cars would be liable for about £25 of tax a year, while a 44-tonne articulated lorry would be liable for a six-figure sum. There probably ought to be a flat-rate registration fee and a length-based element too (which would not be mileage-dependent - you take up the same road space whether static or moving) making for something like;
Road User Charge = A + B * length + C * sum(axle load^4) * annual mileage
Pollution is probably best taken care of by fuel taxes; anything that goes in the tank can be assumed to come out of the other end eventually. Doing this fairly means differential rates on diesel/petrol/LPG, and electric cars mean that the same system needs to be applied to electrical generation and home heating.
Rationalising the tax system turns out to be rather complicated, who would have thought it!