Breathing faster to lose (more) weight?
The rate of CO2 production is normally set by the rate of metabolism and breathing rate is determined by the level of CO2 in the blood.  What you are suggesting is known as hyperventilation. Because blood CO2 plays an important role in maintaining the pH of the blood, hyperventilation can lead to a dangerous increase in blood pH, referred to as respiratory alkalosis.

Apparently one response to respiratory alkalosis is an increase in metabolic rate as the body tries to compensate for the increased rate of loss of CO2. However, respiratory alkalosis is dangerous so I don't think hyperventilation is a viable strategy for losing weight.