Check the range diagrams for the type in question. From that, you should be able to calculate the fuel needed at different weights and thus the operating costs. Then calculate the amount of payload which can be shifted along the route over n flights along the proposed route and divide the operating costs by the amount of payload. Difference in operating cost/difference in payload and there you have it.
Unless you are prepared to make quite a few rather broad assumptions regarding other factors, I’m afraid you’ll end up with a complex answer, largely saying “it depends”.
If you just want the fuel burn, the performance manuals typically have provisions to calculate the fuel used for climb at various weights, fuel flow in cruise and so on.
Or do you want to do it analytically? Then you’ll need to set up the equations of flight for different phases of flight and calculate drag and specific fuel consumption. Again, you will have to make a lot of assumptions and I suspect the answer will be largely “it depends”.
Perhaps if you give us more to work with? Are you interested in the general approach, or one specific type? Is it to be merely fuel consumption or all operating costs? What’s the purpose of the question?
Cheers,
Fred