Unfortunately it's a tenuous link at best:
Southern states like Alabama, Louisiana, Mississippi, and Georgia have some of the highest percentages of black residents in the country. Blacks are generally more impoverished than the average American. People living in poverty are more likely to be overweight and/or obese. In general, you could ignore racial demographics and just observe that these states are among the poorest in the country on average, and that poverty is clearly correlated with obesity.
At the same time, these states are much more rural than many other states in the country. People in more sparse, rural areas often don't have access to a Metro system or public transportation such as buses. This means they're more likely to drive to work. These southern states are generally more rural and have smaller metropolitan centers, so more people commute for work.