NGL, I have no clue why so many say loosing weight is so impossible. In most cases you don't even need to change your diet that much. Sure eating a healthy diet helps, but barring a credible medical condition, exercising a modest ammount each week will see real results.
Even of its only 15 minutes of real exertion that forces you breath thrue your mouth, three times a week and you will see improvements to both your health and energy levels. And that's 15 minutes where your body is forced breath heavily, not a 15 minute workout that leaves you breathing heavily.
Yes the heavy breathing is important. It means your heart rate is up, and your body needs the extra oxygen. And no just breathing heavily isn't going to cut it. Find some activity that makes you move your body and forces you to breath heavily.