That is a myth - for many people, trying to lose weight is counter productive to living a healthy life.

Sometimes sick people are/get fat and sometimes being fat can strain the body. But trying to make your body thinner than it wants to be is also associated with strain on the body.

I am not trying to say, that fatness and health are totally unrelated, but the correlation is not as important as our culture makes it out to be.

This article explains it quite nicely.

https://www.science.org/content/article/obesity-doesn-t-always-mean-ill-health-here-s-what-scientists-are-learning