There have been quite a few studies on the subject, many of which have concluded hormonal imbalances caused by stress that seem to either encourage fat gain or inhibit fat loss.
In addition to the chemical imbalances caused, often emotional eating (sometimes leading to binging) is triggered by stress.
Both exercise and a healthy diet have been shown to improve stress levels. Exercise can stimulate the production of endorphins, commonly known as a "runners high" after a workout. Carbohydrates play an important role in serotonin production, (serotonin has been shown to aid stress levels). B group vitamins have also been suggested to aid stress and energy levels. There are many other examples, I have just picked a few of particular interest.