If it is a partner, friend or family member and you are concerned about their intent then that is one thing as it concerns you and you are personally invested because you care about them. You would already know how to approach the person with care, as you care about them.
It becomes fat shaming, when you don't know the person, and it has no direct effect on you because you don't know them personally and as such, it is none of your concern.
Like for example, people fat shaming Lizzo.. as if they know her. Just because she is famous doesn't mean people have a right to shame her over something that has nothing to do with them. These people should take into consideration that she is surrounded by professionals, be they doctors, lawyers, accountants, trainers, managers and assistants.. she also has a family too.
So, if her team of professionals are ok with what she is doing, then that is all that matters because they are professionals. And the armchair doctors out there should be minding their own health and personal business because chances are, they couldn't do 1/10 of the stuff she does on stage and while on tour..
And if we are comparing their chances to her with respect to health care, then their odds are much worse than hers because she is famous, and surrounded by a team of professionals and Dr. Joe Armchair is not and will likely succumb to whatever condition she would be saved from or their treatment would not be as good.
That said, a lot of these fat shamers who are only concerned about health, are no different from those who swear up and down that they aren't racist but want to use the N word without being thought of as one. These people who fat shame also conveniently forget that mental health is health too, and so, to brutally fat shame or humiliate someone over their weight, or appearance with no regard for the impact their words and behavior will have on that person's mental health, negates the bullshit narrative of them doing so out of concern for that person's health and it is PEAK gaslighting.
Mental health is health too, and just because you can't see the scars, doesn't mean that they aren't there. There are plenty of thin people out there killing themselves for various reasons and using different methods to do so, but no one says a thing to or about them.. it's like as long as they are thin then it is ok.. like being fat is the worst thing you can be as a person.. and these days you never know how your words will impact someone, or how their day went up until that point and it could push them to do something they wouldn't normally do because of it, and that is all the more reason to watch what you say to someone..
So truly, the best thing to do, is if the person is someone you know personally and truly care about someone you are personally invested in, then bring up your concerns in a gentle manner and if the person isn't related to you in any way shape or form, then it is best to mind your business. Sure it would be your right to say what you want about a person, but other people would be well within their right to think that you were an asshole because of it.
Minding your business really is that simple and the people that do so, seem to be the happiest overall, so with all the misery out there, people should be doing this to create their own happiness instead of trying to spread their misery to others.