Registration fees are likely the same or close but when you factor in gas taxes (the original comparison here), the Ford is definitely paying more both based on fuel type and mpg.
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.