Can you be fit and healthy, even if you’re overweight? And will working out, despite the extra pounds, reduce your risk of a heart attack?

The idea that you can be “fat but fit” has long been controversial. While health experts endorse physical activity as beneficial, many doctors view the concept of being “fat but fit” with suspicion.

Now a new study, believed to be the largest of its kind, suggests that even when overweight or obese people are free of health complications, they are still more likely to develop heart disease than their peers who aren’t overweight.

It didn’t matter whether obese people were free from diabetes, high blood pressure or high cholesterol, a condition sometimes referred to as “metabolically healthy obesity.” As long as they were obese, they were at modestly higher risk for having a stroke, at nearly 50 percent greater risk of coronary heart disease and had nearly double the risk of developing heart failure than people who were not overweight and in similar metabolic health.