While a heavier vehicle at times needs more energy - trains are a counter example to consider. Magnitudes heavier, but do not need magnitudes more fuel.
Which comes to Newton's laws of motion, the two concepts of inertia and Newton's second law: "F=ma", come into play. If the course is a straight 100 mile segment with no elevation gain - then the dominant fuel expenditure will be counter-acting aerodynamic drag. When trains haul many cars, the train cars are drafting behind one another, meaning those cars do not need any force to overcome drag, just the lead car needs to do that.
So, places where trains do badly, will be places where weight matters. Urban environments when stopping/starting a lot - trains will keep it slow. Very hilly/mountainous courses - trains "nope" that and require shallow grades. Which goes to show, if you're spending most of your time fighting gravity - then weight is really important, if most of the time is fighting aerodynamic drag, then weight becomes less important as aerodynamic drag decreases. For example, it does not matter as much how heavy a bullet train is, the drag coefficient is a better indicator of overall fuel cost rather than carry weight.