I think that there are two things going on here. And the OP appears to be conflating them.
It is a very bad idea to have only one person who knows how a job is done. If that were not the case currently, then they wouldn't need to have someone shadowing you. It is good and sensible management to have more than one person able to do a job in case someone is off sick or leaves. And I have on occasions said exactly that same thing to a member of staff, because just because the are currently well, or haven't had time off previously doesn't mean they won't in the future. You perhaps haven't noticed, but beyond the usual "people get sick and can't get in to work" there's been an awful lot of people off sick over the last year on account of this pandemic thing. In fact last year I had to instruct one member of my team, who is a bit of a control freak (and that's her description of herself, not mine) to train someone else on some tasks as I'd asked nicely several times and she always had a good reason why not now!
Since that fact, of itself, is perfectly good management, that leaves us only with the weight loss and questions about your health. A totally seperate issue. As a manager, if I had concerns I would very definitely ask the person about their situation. If they assured me that they were fine, I would leave it at that unless I subsequently had reason to continue to be concerned. I quite definitely have experience of staff who've told me they are fine and they obviously aren't, or it gets to a point where it becomes clear they aren't. What I do then depends on circumstances. But I certainly would not ignore it. So I do think that either they have some experience that is causing them to worry unnecessarily. Or they have good reason to worry about you, whether or not that is warranted.
But is it discrimination? No it isn't. There is no law that says that you should be the only person who knows how to do your job. And there is no law that says that managers shouldn't be concerned about your health. If this is bothering you, sit down and tell your manager that your are very happy that you've lost weight, it had been managed by you in a responsible way through diet and exercise, and you are grateful for their concern but you don't have an eating disorder and don't want to be asked that again. Training someone rise to do your job in case your are off sick or leave is their business, not yours, so drop it. You are making yourself paranoid with something that is a sensible strategy.
Of course, got should also consider if your manager really is seeing something that you aren't, because eating disorders are terrible things, and the people affected by them almost never see that they have a problem.