What is the hormone thought to be linked to obesity?

Leptin: You are probably thinking of leptin. If you delete leptin from a mouse, it gets very obese. If you are obese and not a mouse, however, your leptin levels are actually very high (except for some very rare human mutations). So the problem is not inadequate leptin, but a poor response of our brain to our leptin. Leptin injections were tried as a drug treatment, but were disappointing.