I believe the extra yearly fee is to offset the tax on gas used to maintain road infrastructure that all vehicles use.
The report produced an extensive list of equations for describing the data collected from the tests, and from those equations was born the Generalized Fourth Power Law. It’s a rule of thumb for comparing the amount of pavement damage caused by vehicles with different weights, in terms of axle loads:
(W1/W2)^4
In the equation, W1 is the weight of an axle on vehicle 1, which we would compare to W2, the weight of an axle on vehicle 2.
Let’s look at some numbers for comparison.
Consider a standard sedan with two axles and a total weight of 2 tons. Assuming an even distribution, each of its axles would bear the weight of 1 ton. Now consider a semitruck with eight axles and a weight of 40 tons -- each of its axles would weigh 5 tons. The relative damage done by each axle of the truck can be calculated with the following equation, and comes out to 625 times the damage done by each axel of the sedan.
(5 tons/1 ton)^4 = 625
Considering that the truck has eight axles and the sedan has two, the relative damage caused by the entire semitruck would be 625 x (8/2) -- 2,500 times that of the sedan.
- https://www.insidescience.org/news/how-much-damage-do-heavy-... - https://urbanmilwaukee.com/2017/06/22/murphys-law-how-trucks... - https://truecostblog.com/2009/06/02/the-hidden-trucking-indu...
Equating the marginal increase in pavement maintenance costs (due to trucks and heavy-loads) to the overall costs of building and operating a highway is also entirely wrong, but that's a bit tangent the point here.
I'm usually the first to point out the outsized amount of damage and wear attributable to heavy vehicles, but it's still a marginal increase of only one cost component in running a public transportation network.