I think in real life we have a lot of variables related to solve the obesity problem. But I agree that reduce using a car and make everyone use a bicycle/walking will reduce the percentage of obesity. We have to think more.

It entices people to do some physical exercise each day. That (my theory) doesn’t make them lose weight, but makes them gain less weight.

A negative correlation between obesity prevalence and ‘active transportation’ certainly exists. Check the charts on pages 11/20 and 12/20 (page numbers 805 and 806) of http://www.cycle-helmets.com/walk-bike-obesity-rates.pdf

I'd guess that nobody knows because we can't do experiments like that without a ton of confounding variables.