I think that a lot of the comments about fat people knowing they are fat are being a bit disingenuous. What disturbs me about this is that they said he "hates" fat women. That's a horrible thing to say. I would be questioning why they seem to apparently be ok with that attitude. Noone should "hate" a fat person. The word hate is so extreme it is not just talking about a preference is it? The parents commenting on it in that fashion sound like they are questioning why he is with a fat person as though there is nothing wrong with this hatred, not challenging him on this apparent "hatred" in the first place.
At the age he is, he might well have said something stupid and ignorant in the past. Again, I would question more the parents and why they don't see that might be complete immaturity.
So I understand the OP for being offended and not wanted that sort of unquestioning comment and attitude in her life. I also understand the shock of overhearing such a nasty conversation and needing to get away.
On the other hand, the parents learn nothing by not being challenged or told why you are upset. I would respect the boyfriend more if he talked to the parents rather than just cutting them off. He could tell them whatever his attitudes in the past, he's grown up a lot since then and realised it's not the way to be. The fact they are acting like the statements of an extremely young person are set in stone denotes, to me, that they either have similarly poor attitudes towards others on the topic, or else they are very immature themselves not to realise that people learn, grow and change.
The OP might find it beneficial to her own confidence to be able to hold her head up and state her views on this and say why she feels the way she does. There is no reason to feel ashamed. The running away and the cutting off is a kind of hiding which keeps a sense of potential shame in place. Trying to face the situation might be quite a strong thing to do. Although I acknowledge it is a hard thing to do and many of us might not be able to face our own insecurities so head on.
I think the parents should apologise. The people here saying they would comment to maybe should have a look at themselves. You shouldn't invite a person to stay and then gossip about them in the other room in a hurtful way where they could hear. If you have to gossip, at least have the grace to wait until they are safely not in your home! It's the utmost rudeness to invite someone to stay and for them to overhear that! They haven't just had a private conversation in their own home, they have meanly gossiped about a person they have invited to their own home. They have certainly not been careful at all and the casual way they've talked about it doesn't sound like they are criticising their son's past attitudes, but it might be worth at least trying to find that out.