Fat contains long hydrocarbon H-C-H chains (with other stuff at the end). When it’s broken down to release energy, it combines with (3) oxygen O2 molecules, making H=O=H (water, H2O) that you sweat, pee or breathe out, and O=C=O (carbon dioxide) that your breathe out. Carbon accounts for significantly more of the weight than the hydrogen and it’s in this sense that you breathe it out.

If you breathe significantly more without exercise, you’ll hyperventilate, which I’m sure is even less fun than the exercise in lengthy doses, and I don’t think you’ll lose weight.

Not effectively. You’ll just have a lower concentration of CO2 in your exhaled air. Maybe it’ll stay the same with the increase in exertion by breathing more, but that’d be a good way to estimate how little energy your breathing consumes compared to proper exercise. And after all that, exercise is pretty slow to burn calories as well. The good news is your brain burns calories by thinking harder, an activity we’re both now involved in

This guy thinks so, but you also have to do cold plunges. And is more about converting your fat into a better kind of fat.

https://www.wimhofmethod.com/