I'm going to go against the grain here and say NTA - hear me out...

Firstly, I think you could have handled it better. Take this as a learning opportunity to voice your feelings. Try take a deep breath and say "mum, when you talk negatively about your body it really hurts me....". The calmer you can approach situations like this the better response you should get.

However -

It's not your job to take into consideration your mum's body image issues.

You can be empathetic, yes, you can tell her she's beautiful and compliment her, yes -- but if you're struggling with your body image this is something you mum needs to really help YOU with. As soon as you were obviously affected by her words she should have taken the opportunity to find out what was really going on.

I feel firmly that there's a parent child responsibility and, whilst you should want to be kind and treat your parents with respect, it's their job to guide you into adulthood and be your emotional support, not the other way around.

It was probably a throw away comment that your mum said, said with no harm at all. But she should now realise that there are issues happening deep down with you and this is the time to address them.

In this world you're going to be met with weight and body image negativity everywhere you go. It would be great if you could talk to a therapist about your issues here, before they become much worse.