If you just increased willpower to overcome this much stronger hunger drive, you'll have increased will power beyond any kind of equilibrium with the other (weaker) survival instincts, thus increasing the probability of some unintended problem.
The solution isn't to just increase willpower, as will power isn't lacking and increasing it more could cause problems. The solution is to address the real issue: the body's exaggerated response (i.e. releasing hormones which cause the sensation of hunger even when the individual is overweight) to fighting caloric restriction.