Gen Xer here so I came up in a fatphobic society. No such thing as SA/BP and it was open season on fat people in the media — truly the last allowable prejudice. My mom was a classic Boomerexic, proud of how little she ate and she'd point out every fat person with disgust and/or ridicule. My dad was less overt about it but made his fatphobia known here and there. Meanwhile I was basically born an FA, hiding "before" pics from tabloids under my mattress, drawing fat women compulsively, mooning over Mamas and Papas album covers lol and so on.
My first GF was in junior high. She was fat for the early 80s but "curvy" now. I was terrified to tell my mom about her or bring her around. Then one day my mom dropped me off at a friend's house and my GF was out front with a couple other friends. She ran up and hugged me before my mom left. I figured I'd get some kind of blowback when I came home but my mom was shockingly cool. Some light teasing — "I didn't know you had a girlfriend", etc but nothing about her weight. Later on my mom soured on her but that's because she thought she was trashy lol, never said anything about her being fat. That said, she continued making comments about other fat people so I was still a bit on edge.
A few years later I had my first real GF. She was the second fattest girl in our class, which back then translated to 5'2" and 180 or so. Again I was worried I'd get blowback or they'd treat her badly but no, everything was cool. We dated for two years, went out to dinner with my parents (separately, they were divorced) and so on and there were never any issues. Both complimented her on her looks (she was actually very pretty), and my dad told me privately he thought she was hot lol. (Yes, she was 16-17 at the time. Boomers.)
I did take some shit from friends when we first started dating but then when the relationship got more serious they backed off and she became "one of the guys." Granted, teen boys will pounce on pretty much anything and I dished out my share of insults, appearance-based stuff as well. I went to a very liberal college where even in the 90s no one would dare insult or ostracise someone over weight. I had a close friend at the time who told me my being an FA was related to low self esteem, which kind of sucked, but otherwise I can't remember friends ever having an issue with my partners.
Ten years later my wife was the next woman I brought home and she was much bigger than the others, 5'3" and 230-260. There were no big issues but a few minor ones. My wife picked up on my mom's incessant diet talk, which I explained was normal for her, sadly, though my wife insisted it seemed kind of pointed. Unfortunately I didn't take it seriously until the first Thanksgiving we had together, at my mom's house, where my mom served her notably smaller portions than anyone else (except herself). My wife later told me this was backed up by more diet and "health" talk. Granted, she'd gained a bunch of weight the year prior so she was extra-sensitive herself but still, it was obvious.
The next day I took my mom aside and told her to cool it. Of course she insisted she was being normal with her, and that "women generally eat less," but she got the message. We were married seven more years and there was no more BS from my mom.
There have been fat partners since then and while my mom hasn't met them, she's seen pics and will say "very pretty" and so on. No insults. And FWIW, with societal changes recently where fatphobia has been elevated to bigotry like racism and homophobia, she's toned her shit WAY down. I haven't heard her comment on someone's size in years at this point.
Dad was super-cool throughout, though once he realized the pattern with my partners he would joke around with me here and there. Thing is we're more like friends as adults so it's like the ballbusting male friends do with each other, and never directed towards a specific person in my life. More like we'd be walking down the street and my dad would see a fat woman and say "there's one for you." I think he's actually kind of fascinated by it but it's too awkward to bring up directly.
So I guess the moral of the story is that despite their rhetoric my parents put my comfort and happiness and that of my partners over their own prejudices. I imagine people say shit behind my back but that's their business. I do the same lol.