I really don't think weight has much of a role. Lots of heavy cars get pretty decent fuel mileage while it's easy for older cars/small trucks to get worse mileage while being significantly lighter among other reasons to not consider weight much.
More weight is more effort and more effort is more fuel consumption. It easy to move an empty wheel barrel around all day compared to one full of dirt. But I'm sure your body will consume more fuel doing it same as your car. Every hundred pounds you drop off your car is something like a gain of 10 hp and an engines hp is directly related to the amount of fuel it burns.