How does body fat leave your body?
Many of the statements in your question are false, including your ideas about waste products.

Ultimately, fats, just like carbohydrates, end up as water and carbon dioxide if they are used in cellular respiration for energy. The reaction path is different, but the ultimate reaction products are the same as you would get from burning fat in a fire: reaction with atmospheric oxygen oxidizes the reactants to carbon dioxide and water.

This is the reverse process of photosynthesis, where carbon dioxide and water react to form sugars, with oxygen as a byproduct.

The mass leaves the body as exhaled carbon dioxide and as metabolic water through the urine, vapor in exhaled air, etc.