The answer to this question is not as simple as it might appear. To me, it's not a "yes" or "no", but a resounding "sometimes". Before you think that is a wishy-washy answer, of no particular benefit, I'd like to tell you why I believe this, and how you can best translate the answer to this question to your own personal health.
Before we had the term BMI (body mass index - that ratio of height to weight), it was hard to "size yourself up", to figure out how your weight was related to health risk. We only had those insurance charts - and surely we were all "big boned"! Decades of study have shown a relationship between increasing BMI and health risks like high blood pressure, diabetes, and sleep apnea, depending on which category you were in. Sounds like an easy connection - right? Not so easy, though, in real life. Population statistics don't always connect to the individual. While BMI is a useful guideline, it doesn't take body fat into account (only height and weight). And that's where this debate comes in.
A small portion of the population (think some professional athletes, trainers, and celebrities) have a high muscle mass, and low body fat. That's why a measure of body fat is also essential, when it comes to sizing yourself up, if you believe your increased muscle mass is contributing to your weight. For a woman, you'll want a body fat of less than 23%, and for a man less than 18% to be in the "healthy" range. So, if your body fat is lower, and you are in the overweight category, this is one example where being "fit" and "fat" are compatible.
Most people don't fall into that category, and are those who both struggle with weight loss (and work just to not gain!) and are overweight or obese. Here is where I'd like to clarify that this is not an "either/or" situation. Abundant scientific data show that those who are in this category, and exercise regularly have health advantages related to improved cardiovascular performance, and other health pluses. If you struggle with your weight, for any variety of reasons, it's important to sustain physical activity (with your doctor's approval), even if it's not associated with weight loss. Improved health is not only related to the number on the scale. Physical activity, even without weight loss, is a plus.
Like most things in nature, there are no absolutes. Healthy eating and regular exercise are habits that support good health, no matter what your size.