There's a lot of evidence you are right. Elderly grossly overweight people are rare--probably for a lot of good reasons.
Zig Ziglar used to advise people to ask their slender doctor for weight loss advice. And if their doctor is actually fat, get a new doctor fast.
His doctor said in his office: "With my diet you will be happy to learn you can eat everything you want." Then he pulled out a sheet from his desk. "This is a list of everything you're going to want to eat."
“The ones who make it into their 90s were thin, or fit,”
Leon Askin is an exception. (General Burkhalter)
He lived to be 99 somehow.