A clear and effective video from Vox explains why exercise is not directly a cure for overweight. The video's message -- rightly -- is that we should pay close attention to food intake and the quality of the food environment.
The video does note that physical activity has strong direct effects on health. Nonetheless, I would have emphasized the benefits of physical activity even more strongly than the video does.
My first reason for giving physical activity yet more credit is a bit geeky. Much of the research literature uses regression models where a weight measure is the outcome variable and physical activity or exercise is the main explanatory variable. To make sure the analysis really reflects the "effect" of exercise, the studies include additional control variables such as food intake and general health. Yet, when we step up our physical activity, we may experience improvements in health, mood, and feelings of self-efficacy. Including explanatory variables for food intake and health status may risk "over-controlling" for other factors. We may eat healthier when our mood is good. We may avoid periods of poor health and inactivity that lead to weight gain. Perhaps stepping up our physical activity deserves some of the credit for improvements in weight that are being picked up by the control variables.
My second reason for giving physical activity yet more credit is more superficial. For some people who seek to lose weight, the ultimate goal is to look better. I have mixed feelings about whether this is good psychology, but it does seem to be common. Stepping up physical activity may affect posture, muscle tone, and confidence, making people look better in ways that the scale may not register.
But the video certainly is right that researchers in recent years have become more careful about not over-promising physical activity as a complete weight loss program on its own.