If you ever go on 4chan.org/b/catalog and search for threads titled "FB/IG." It is an incredibly common thread and to provide a brief synopsis (so you don't actually need to visit the underbelly that is /b), these threads are dedicated to pictures of scantily clad girls all taken from their social media profiles. It's VERY common in fact if you go there now I'll bet you'll see one of those threads close to hitting the 150 image limit.
For the sake of transparency and helping your situation I'll be honest, I used to do EXACTLY what your partner did and while I can't speak to him, I can share my background and headspace so that you might understand where he's coming from. I look at these FB/IG threads instead of people I know. It's a middle ground and my fiancé knows I look though she'd rather I didn't.
It started when I was in high school. I used to jerk off to the hot girls in my class's Facebook photos. They would post bikini pics or pics from a weekend party doing sexually suggestive things. I would look and jerk because puberty and because it felt dirty. The girls in porn are distant and I knew they were doing it for the money, real girls aren't doing it for money and that's part of it. Then the pics would get taken down bc some of the content was embarrassing to the person tagged in it or person who posted it. So I started saving these pictures when I saw them immediately posted, which my girlfriend (now fiancé) discovered and her reaction was similar to yours. "You don't think I'm attractive." "I don't look like the girls you saved." "You wish you could be with them if you had the chance." And all I wanted to do was shake her and say "ITS NOT ABOUT YOU, I LOVE YOU THEY ARE JUST A FANTASY! The moment I cum, I'm done and don't think about them."
I understand where the insecurity comes from. My girlfriend at the time had recently gained weight and although I was employed I was in between projects so I was depressed and we weren't having sex. She took it as my lack of interest in her and that was the furthest thing from it. You recently gained weight from a pregnancy and I'm taking a guess that your sex life might not be where it used to be. My fiancé also told me at the time she felt threatened that I might leave her and that I was looking at these girls as potential partners, which is not how I saw them AT ALL.
Long story short I deleted girls I was friends on FB solely for the purpose of jerking to (sometimes you happen to be friends with attractive people), I look at the threads on /b as a middle ground and while I still occasionally do save images from those threads, I'm trying to stop because I know how it hurts her feelings. To me, it sounds like a fantasy of his and so long as he hasn't done anything with this person I don't necessarily think it's a deal breaker.
He's willing to work with you. He loves you and apologized. While neither you or he probably can't stop a sexual fantasy or preference, I think you should tell him how this makes you feel and why you're feeling insecure and why it hurt you. I don't think it's unreasonable to ask him to unfriend/unfollow this person. I think it might even be helpful to point out the threads on /b because then at least he gets his "real girl" fantasy out of his system without actually knowing the person IRL.
Anywho, I hope my devils advocate perspective helps. I don't think you should cast the father of your child out for this.