These aren't jokes, they're jabs. The way he's turning it around on you when you say that they upset you so that you end up apologizing and trying to be "better" is extremely manipulative and emotionally abusive. Not to mention using your anxiety to instill doubt in you that you're the one in the wrong....that's not okay.
If he respects you and cares about your feelings then he wouldn't continue to find entertainment in things that make you upset.
For what it's worth, I invested almost 2 decades into someone who made these same types of "jokes", and no way of phrasing how and why and that they bothered me made a difference. And then they got meaner and more public (like loud, derogatory put downs in the grocery store), and the anger escalated (he would get mad if I was bringing up that those jokes hurting me "again" two seconds after a new one because he was tired of hearing about it, or I didn't anticipate what random thing was going to set him off like whether or not I was supposed to remind him about a turn coming up unprompted - both options were always wrong, etc). I'm out of that now, but I'm never going to get those years back. I also have anxiety now and didn't before (living constantly on edge and eggshells isn't great for your mental health).
It may not escalate for you, but it could. I was in the same place 3 years in.
My honest advice to you is to get out of there. People don't change unless they want to, and often times that takes therapy and they can't do it on their own long term with just willpower. How he's handling it when you tell him to stop is very telling about how much he wants to change and where he feels the fault lies. Be with someone that lifts you up and doesn't take joy in tearing you down.
Please also consider how regularly second guessing yourself and being chastized for standing up for yourself is going to effect you mentally long term.
r/emotionalabuse might be a community worth checking out too, if you haven't already. They should have some good resources and advice over there too.