I hate it when people say others are 'fat' they may be overweight, but they aren't fat, fat shouldn't be used as an adjective. Fat is something they may have but not what they are.
For someone with serious body image issues, I think nobody should ever comment on people's appearance, I even take compliments pretty badly sometimes, so it's best not to comment at all.
Most people think small, thin, petite is a compliment, I doubt they would mean anything by it. Unless it is a dig comment like one of the previous posters getting told to eat a mars bar, but then again some people would call that 'banter'
If someone says I look well, I do a Stacey from Gavin and Stacey - I think they mean I'm overweight or put on weight.
I've been told I'm too thin most of my life, then I put some weight on and an old neighbour of my parents, that hadn't seen me for awhile said 'Hi, OMG it is you, only recognised your face, haven't you filled out' I was so gobsmacked I didn't have time to react.
I've had people openly tell my partner that he has put on weight. Family and acquaintances, sometimes they don't look so hot themselves, but I would have never commented on it. I always try to stick up for my partner when I can (not that he needs me to, he would rather ignore it) He says it doesn't affect him but it can't be nice to hear from anyone.
BMI is just an estimate, it doesn't take into consideration large muscle mass and measuring isn't perfect either as some people that are size 10 are much heavier and different shape to another size 10 lady.
You can be a healthy weight but not healthy, if you eat junk food all the time, you probably have quite a bit of fat around your organs.
You sound like you are bothered by the comments but not your actual weight. If you are maintaining a decent weight and it fluctuates a little but overall you are around the same, you sound okay. I'd be concerned if you kept dropping weight, which is when you should probably see a doctor and/or dietician about it.
I would advise just responding honestly and abruptly to people who comment that you aren't happy about, that way they should get the message and not comment again. If you giggle and brush it off, they may continue making jokes or comments.
Something like 'Well I wouldn't be so rude to comment on something like that' or 'What makes you feel that you have to comment on others appearance?' You aren't being rude or unkind, just making them aware of their behaviour and comments not being appropriate.