Gluttony. Huge portions of unhealthy food, but that's the same in lots of places without as big an obesity problem.
I think it's a sedentary lifestyle. I think, though, the main reason for obesity in America is the layout of the American city. You can't really walk anywhere, you have to drive. In Europe, outside of the absolutely enormous and mainly-modern-style (and consequently North-American-style cities, ie London, Moscow) it's difficult to drive somewhere. The roads are narrow, there's no parking, everything is chopped up by districts with pedestrian-only streets. It's congested, it's unpleasant... it's far easier to to just walk.
If I wanted to drive from Vratnik to downtown Sarajevo it would take me, in the middle of the night, without another car, about 30 minutes to reach the street nearest to downtown that allows cars, and park. In the day time, even on a holiday, it would take at least another 20 minutes to find parking and I'd be a much more significant distance from downtown where I parked.
If I walked... I could walk for about 15 minutes to a tram stop, take a tram downtown and be there in less than 10. 25 minutes. That's why we walk so much, and I think that's the single biggest difference I've noticed in European vs North American life.