Yes, you are fat shaming if you mention they are unhealthy and overweight. The idea that you are in the wrong for pointing this out is mind-blowing to me.
While it may not be an effective means of changing their behavior it is a valid means of framing conversations around what is desirable and healthy. If we continue to allow peoples feelings about how they feel override what we objectively know to be good we will be on the fast train to hell.