Yes, it’s possible to be obese and still be healthy and fit (but don’t try it). A study of over 43,000 people found that a significant subset of obese individuals are metabolically healthy, and fitter than other obese people.
The researchers think that the difference has to do with exercise: more of it helps everyone—including the obese—develop healthier body systems, which yields metabolic health. Of course, exercise has benefits even broader than physical health, like reducing depression, anxiety and the effects of stress. So get to it!