Estimate fuel cost of extra load.
Carrying weight costs fuel through rolling resistance and the energy needed to accelerate the extra mass, at a well-established rule of thumb near one percent of economy per hundred pounds. Where the load sits matters more than most people expect: on a roof rack, aerodynamic drag adds roughly five percentage points on top of the weight penalty, which at motorway speed usually dominates the weight effect entirely. The extra fuel is the difference between the loaded and unloaded consumption over the same distance, so it is always positive or zero.
Economy penalty
Penalty = pounds / 100 x 1 percent, plus 5 percent if the load is on the roof
Extra fuel
Extra gallons = miles / loaded mpg - miles / unloaded mpg; cost = extra gallons x price
Yes, and substantially — the drag penalty is about the shape, not the contents. An empty box or bare crossbars can cost 5 to 15 percent on the motorway, which is why removing them between trips is worth the ten minutes.
No. Weight matters most in stop-start driving where you repeatedly accelerate the mass, while aerodynamic penalties dominate at speed. The rule of thumb used here is a mixed-driving average.