Not sure where you are but in Indiana, gas tax for unleaded is 36c while diesel is 62c so on a per-gallon basis, that's an additional +72% in taxes. Back of the envelope: Civic at 30mpg pays 1.2c/mile vs SuperDuty at 15mpg pays 4.13c/mile so the multiple is closer to 3.4 vs 2
So yes - assuming registration fees are comparable and mileage is comparable - the SuperDuty should pay more.
The lightest SuperDuty has a gas engine. Diesel SuperDuty fuel economy is a bit better, but the vehicle also weighs more and is likely to be carrying/pulling more. But regardless of whether the multiple is 2 or 3.4 or somewhere in between, it is a small fraction of the added road wear.
By the fourth power law, an unloaded diesel Superduty creates ~22x the road wear of a honda civic. Loaded can be 100x more.
+700lb (+25%) => 2.25x damage +2800lb (+100%) => ???x damage
Your story doesn't provide a formula, but seems obvious it is much, much greater than 2 - this isn't a linear relationship
And that's the very lightest SuperDuty model, unloaded.