am I overreacting?

Sounds like your Mum is overracting rather than you.

She just makes me look like the bad person and it’s just so wrong if she doesn’t like his weight how it that my problem I can’t keep hearing the same stuff all the time

Have you tried something like "Mum, I appreciate that you think X should lose a bit of weight, but you've mentioned it multiple times now and it's getting to the point where it's upsetting me.".

I have many times and she knows I don’t like her saying it she just goes oh I’m only saying it I’m joking and I told her you’ve said it so many times

My mum got angry at me because firstly she always goes on about my partners weight and literally he’s not obese or anything he’s just a little bulky because he goes gym. But anyways there was a man on tv and my mum was like oh if your partner lost weight he’d look like him and my mum was like you should bet him to do that challenge and I said oh it’s fine he looks okay to me if you guys want to say these things you can say it directly to him. Honestly I’m tired of hearing this they’ve said it so many times about his weight like it doesn’t bother me but it bothers my mum. She got angry and called me ‘sensitive’ that’s not what a mum should be doing I feel like **** it’s just wrong