No tax I've seen is anywhere remotely close to following "fourth power law" on axle weight[]. And especially so for gas taxes, as the gas/diesel cost tends to be closer to linear with weight.

Usually what happens is smaller cars subsidize everyone else due to paying a disproportionate tax vs axle weight^~(2-4 depending on fatigue pathway). Depending on tax structure possibly pedestrians/cyclists too but they are usually parasitic on tax basis.

[] https://en.wikipedia.org/wiki/Fourth_power_law

Agreed, tax based on damage to road, and then tax fuel the amount it costs to clean up the pollution the fuel causes, and then use the money to clean up the pollution it causes. Then who cares if you fly your private jet, or giant car, you just pay for it.

Side effects include: reduced pollution, and cheaper ways to clean up pollution