The mechanisms in the body are not heat engines. The stuff is so tiny that it works basically by reshuffling molecules, so the traditional concept of efficiency doesn't really apply, as the amount of stuff that happens is given by integral math. You get this amount of charges from reshuffling this amount of molecules. The type of stuff that can be done is limited by how hard the stuff sticks together.

Anyway, the core problem of obese bodies is that they can't produce energy. You can't outwill it, the reshuffling just isn't happening, and there is actually no great reason to believe that fat tissue is some kind of fuel tank, rather than a mass of broken cells.

Also, the body can just reshuffle the molecules in an idle mode. You don't need to spend the energy on moving around.