This is the stupidest concept application I have ever heard and you are not the first person to do it. You are likely following the uninformed logic of someone else so I will not fault you directly.
All vehicles will have their fuel mileage impacted by the weight of the vehicles. All larger and heavier vehicles will by default pay more from the simple act of being used. The roads are repaired with taxes collected from fuel sales and either more friction from their foot print (less aerodynamic) or power needed to overcome the extra weight will cause more fuel to be consumed thereby already increasing the amounts they pay by default. There is no way around it.
If we compare two identical drives made at 100 miles a day, 5 days a week. and a hybrid car gets 45 mpg average of fuel use and a 1/2 ton pickup truck uses 20 mpg (both a low end combined city/highway average for the vehicle types), we will see how much of a difference there is. Let's take California's fuel tax for comparison sake. California has a 35.3 cents per gallon state fuel tax and an18.4 cents per gallon federal tax obligation (most of which they get back in highway trust fund projects). So the hybrid drives 500 miles a week at 45 MPG and uses 11.11 gallons of gas. The Pickup truck drives 500 miles a week and uses 25 gallons of fuel. In a weeks time, the hybrid pays $3.92 in state gas taxes and $2.40 in federal gas taxes. This is $6.32 a week in total or $328.64 for the year. The truck pays $8.82 a week in state and $4.60 in federal gas taxes. Combined, this is $13.42 a week in gas taxes or $697.84 a year in gas taxes for the same amount of driving.
Notice how the heavier pickup is more than double what the lighter hybrid pays? This is compounded even more when larger trucks are in the mix and more fuel is used. And this is before the various sales taxes which can be different county to county are applied but those increase with volume also.