I have dated very few men who were overweight. I think only two, neither of them very overweight. One had a beer belly, the other one was really just very chunky, not really "fat." I've dated several men on the other end of the scale, way too skinny for my tastes.
I'm not opposed to dating fat men or physically imperfect people, but when I'm single a lot of men ask me out and I tend to choose the man who has the best combination of qualities that I like first, one of those being attractiveness. For example, when I broke up with my previous boyfriend, in the two weeks before TheBoyfriend asked me out, 12 male friends that I had known for 5 or more years confessed that they have been carrying a torch for me for years and they thought that we would be perfect together. Yeah, nice ego stroking moment, but none of those friendships really survived, and I'm still working on trying to save the one friendship that I think may be salvage-able with a man I've known since I was 19 years old. I was holding out for TheBoyfriend because we had serious chemistry and he's sweet, smart, funny, hardworking, successful, etc, etc, etc. And yes, he's got a great body, too, and that had a lot to do with my attraction to him.