is fat heavier than muscle
Muscle does not weigh more than fat, any more than lead weighs more than feathers. A pound is a pound is a pound. Where the misunderstanding often comes in is that muscle is much more dense than fat, so that, by volume, it seems to weigh more. That is, a pound of muscle occupies less space than a pound of fat. In addition, because a pound of muscle burns more fat than a pound of fat, even at rest, by increasing your lean muscle tissue mass, you're helping your body burn more calories. But back to your question.