maybe it's not in fashion to listen to the CDC in these times, but:
"Obesity is a serious concern because it is associated with poorer mental health outcomes, reduced quality of life, and the leading causes of death in the U.S. and worldwide, including diabetes, heart disease, stroke, and some types of cancer." [0]
Except "associated with" is just another way of saying correlated, not the cause of. A lot of people would live healthier lives, both mentally and physically, if we gave up on trying to fight obesity itself and just spent all our effort getting people to exercise.
They won't die to it because they don't have it - while the percentage of people who are obese in the US is higher than other parts of the world, it's still not a majority.
No the majority of people will die from, surprise, being old. Being obese might be correlated with dying a little less old, but the cause of death is still, fundamentally, being old.