But then why do it yourself
Because we do what we recognise. You are now doing it to yourself, too. That's what happens. When we become adults, it means that we don't need our parents anymore. Not because we don't need parents, but because we are old enough to be our own parent. So now, the parent part of you is parenting the part of you that needs parenting, and it's copying the style of parenting that it was shown. That's why you judge yourself negatively. So, you could equally say 'Why do it yourself?' with regard to you, and your internal treatment of you. You are doing exactly what your Mum did, in the negative comparisons with other women. The 'but she's slimmer' comment is a perfect example. You don't like comparisons with other women, because you grew up with them, you now do them to yourself, and they're never favourable.
You need to tell your partner you don't want him to do this any more, because you don't like the way it makes you feel. He doesn't need any more detail than that, unless you want to give it to him, and it's not a discussion. Make it clear to him what it is that he's doing that bothers you, and ask him to stop because it makes you uncomfortable. If he loves and respects you, that will be the end of the issue, or very nearly the end, barring a few slip ups whilst he gets the hang of it. You are allowed this sensitivity. It is part of who you are. If he understands what he's doing, and you tell him you don't like it, he'll stop. If he doesn't, rethink the relationship altogether.
Imagine if he said he didn't want you to tell him he had lovely eyes/hands/face/whatever, because it upset him. Would you try to stop, or would you carry on, because he was being silly, and you were being nice?