Is there a correlation between car use and obesity?
Yes. But car-use is correlated with broader lifestyle changes, more sedentary occupations, and the ready availability of highly calorific manufactured foods. These all conflate. Go back two generations to my grandparents, fast food was the local chippy (which you walked to) and was a special treat, there weren't any drive-thrus, they cooked (not well), and my gran went to shops every day with her little shopping trolley, even in her nineties. They had biscuits and snacks but they were firmly treats. Even in my childhood, if I was hungry, you waited for dinner time and there was none of that modern negotiation, as a kid you ate what was served, no matter how foul. If you didn't, you stayed hungry. I watch parents with kids now, bribing their kids to eat stuff.
Oh Olivia won't eat vegetables. There's been an attitude swing in our relationship with food.
It's a valid point that you can't exercise away a bad diet and people will respond differently to food (and this will change over time, I could eat a kilogram bag of biscuits when I was ten, I couldn't now). You have to run a long way to burn off a Mars bar (probably about an hour on the bike). But exercise and activity certainly helps control weight and prevent the gain in the first place, and of course, it has a huge impact on cardiovascular fitness. Healthy, fit people generally live longer, and more importantly, those additional years have a good quality of life. It's also a valid point that the little things add up.
One of the changes is, of course, getting people invested and involved in their health. It's proactive and has to start young, it's too late if you turn up at GP at 45 because you have high blood pressure and the early signs of diabetes. It's very difficult at that point to address the issues.