Willpower is exactly why they eat more. They feel a pang of hunger in their grossly stretched out stomach and can't resist eating.
The drug does not remove fat. It removes the feeling of hunger. Assume both groups have little willpower (they are fat after all). The control group feels hunger and continues satisfying that hunger with food as they have no will power. The group with suppressed hunger from the drug also have no willpower, but since they feel no hunger they eat normal amounts.