Are there good breathing exercises for weight loss?

No, not really ... There is not a breathing exercise that burns calories to help lose weight. Breathing is quite effortless, and uses few calories. However, some people eat a lot when they are anxious, depressed, or otherwise feeling stressed. If such a person uses breathing exercises for relaxation, meditation, yoga, etc., he may feel better and eat less . . . And lose weight after all!
I don't think so.. Weight loss requires taking in fewer calories than you burn. The best was to do this is to eat a bit less and do (exercise a bit more). The only exercise than "burns" fat is aerobic exercise. The act of breathing does use energy, but in general, it is not part of a weight loss program.