Well, I can kind of see how exercise is a physical stress. We are pushing our bodies. Inherently stressful. Emotionally, we may feel it relieves our stress. We feel the benefits of all those yummy endorphins.
I do think the whole, "Stress makes you fat," is one of those theories out there that has some scientific merit but, well, my guess is stress + eating too much + not exercising enough makes you fat. Kind of like how they say that not getting enough sleep "makes you fat." I haven't gotten enough sleep in seven years (age of my oldest child) and definitely not in the last 19 months (age of youngest child). And when I eat too much and don't exercise enough, I get fat. Then I blame it on the lack of sleep -- heck, all the magazine articles say so!
Be good to yourself -- sounds like a lot of work and exercise -- but then we don't succeed by napping all day, do we?