It's probably both. One big predictor of near-term all-cause mortality is the simple question, "can the person comfortably walk for a mile or two at a brisk pace?" (Barring existing mobility issues ofc)

Exercise helps to keep your body less stressed in many ways during its normal day-to-day life. It's good for your immune system, your circulatory system, your digestive system, and even your brain.

A few extra pounds probably won't cut your life short, but chronic heart disease or blood clots or being bedridden in old age definitely can.