I have found little so far to help me with this in the way of forumla but as I understand it fuel use will be some sort of combination aircraft type, distance, pax (and pax weight), Cargo, empty mass, fuel carried, fuel not burned. I am not sure however of how these figures can be put together to show how fuel use will reduce with an increase in weight though!

Start from engine efficiency and build it back up. The propulsive efficiency of an engine might be around 0.70. The thermal efficiency might get up toward 0.5, giving overall engine efficiency of 0.35 or so.

Figure out your aircraft L/D for various stages of flight (well, estimate it). You know the energy content of fuel. Decide your payload weight. Add in your divert fuel and you have your end-mission weight. Therefore you know the required fuel consumption at the end of flight.

Work backwards towards the start of the flight (mission length is up to you), accumulating the fuel needed to finish the flight which will add to your lift dependent drag.

The Breguet range equation may be useful for the cruise portion of flight.