Leptin is made by adipose cells, and its absence stimulates feeding, so raising its levels would trick the body into thinking that it had already eaten. This would reduce hunger and help the obese eat less.
Work Step by Step
Look at the role of leptin--signalling that eating has occurred. Adding it exogenously would send a false signal to help the obese "think" at a metabolic level that they need to eat less than they do otherwise.