A remarkable fraction of your energy consumption is spent on basic maintenance, and of the rest, far more than you'd think is spent on the brain. Your body is extremely efficient, by engineering standards, but that includes locomotion.

Exercise is still a good way to drop in weight, but not simply due to burning up the fat; that could happen anyway. What seems to be happening is that the exercise improves the body's budgeting logic, probably by putting you back in a regime evolution already dealt with.

The way to drop in weight isn't to exercise (as such), and it isn't to eat less. All the logic that says those count, is valid, but you have to account for the body fighting back. The goal is to eat less because you don't feel hungry, not despite feeling hungry. Very few have the willpower to literally starve themselves.