I have never heard another source citing Oxygen/CO2 exchange as a factor for weight change, again, please site a source. O2 levels are certainly a factor of cardio health which can be correlated to overall health and weight.
Yes, macros also matter. But, nothing matters as much as the simple math of calories in/calories out. Its disingenuous, borderline irresponsible, to suggest otherwise.
https://www.bmj.com/content/349/bmj.g7257
(note I don't totally agree with this paper, and agree that if you eat almost no food, you will lose weight, and that exercise definitely seems to increase the metabolic rate and increased mass exchange in the lungs. Like I said, it's complicated).
I'm not being disingenous or irresponsible- I'm describing mainstream science based on biophysical data.
Apologies for the tone in my original comment. I misdirected work stress this morning.
To be clear, I think your instinctive reaction is correct. It would be extremely silly for someone to read this analysis and conclude that they'll lose weight if they learn some special breathing technique to maximize CO2 output. The point is that "calories in - calories out" as a diet strategy is the same kind of error.