You’re not shaming fat women by making a decision for yourself, for your own health. It’s ridiculous that people are even trying to make you feel bad about yourself. It would be valid to not lose weight, and it’s valid to also lose weight.
If people feel upset seeing you lose weight, inherently JUST BECAUSE you lost weight (not because in doing so you were rude to them or treated them worse than before) then that’s their responsibility. In that instance you haven’t “hurt” them by simply living your life and making choices for yourself. They are choosing to react to your mere existence in the world as though it’s an insult to them. That’s THEIR problem.
Diet or don’t diet. It’s up to you. But you don’t have to feel guilty for whatever choice you make.
So long as you don’t go ahead and assume your choice is right for everyone, that’s fine.