The study (which needs significant followup to create usable results) could have a number of interpretations, including:

*conclusions not fully supported by the data

*obesity leads to less enjoyment of motion

*obesity leads to fewer social opportunities to engage in sports

*low socio-economic status leads to obesity and to inactivity (due to insufficient access to parks, to parents who force you out of the house, etc).

*People don't record their activity levels every day, so their estimates are colored more by measurable factors (body weight) than by unmeasurable ones (how much they actually moved).

I'd hesitate to read too much into this study.