Good question, but I suspect all 1/2 ton trucks made today are class-II, so they probably all pay the same price. There may be some older 1/2 ton trucks that max out in class-I, but probably nothing made today. Some sites have the class-I limit listed at 5000 lb, but that last link from LHF2019 shows it at 6000 lb.
Where the waters may get a bit more muddy, is that I think you can register a vehicle lighter than it's GVWR, as long as you don't load it above registered class. This would probably only be worth it on a dedicated work truck of a higher class, where the fees are a bit higher, if you know you'll never be loading it above a certain weight. Classes 10 - 25 run $1k - $3k/year, the big boys club.
Down in 1/2 ton or 3/4 ton, these fees aren't exactly hundreds of dollars. It's close to $80/year for class-I, and just over $100/year for class-II. The total difference is $28. The big jump is going from a passenger vehicle ($37) to any pickup truck ($77 - $105, class-I / II).
Also, I was talking about fees, not fines, but I wouldn't be surprised if fines (eg. speeding tix) were also scaled with class. It would make sense to hit a heavy truck harder for excessive speed, than a sprite little Porsche 911.