This is long as hell. Sorry.
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I think there are two things going on here. On the one hand, yes, on average men do tend to prefer women who are HWP. On the other hand, men also tend to prefer confident, sexy, sensual women. So, IMO, if in your quest to become HWP, you let other WOMEN beat you down and diminish your confidence (which in turn will effect your overall sexiness and sensuality), you are worse off than a heavy woman who is confident. IME, well-adjusted PEOPLE (men included) don't really want to spend their time battling with the insecurities of a friend or lover.
It is a fact that big woman marry. Do they marry at a lower rate? Are their marriages less successful? I have never seen a statistic or study showing that, and I'm sure if such statistics existed, they would have been linked to a thread on this site a long time ago.
It is also a fact that big woman have and can marry good quality men. However, if you have decided that a quality man can't possibly be attracted to you at size 16 and up, well, you've already framed your reality, so poor results will naturally follow.
I think that it is very unlikely that a size 16 plus woman who believes that she is unattractive and that "quality" men are "out of her league" is doing the necessary in terms of flirting, and actively putting herself in the line of sight of men who she feels are "out of her league." Plus, to the extent that she is rejected by such men, she probably blames her weight for those rejections (even without concrete evidence that her weight was the problem) and likely shuts down even more. It becomes a self-fulfilling prophecy, and yes, she does eventually become invisible to the men she wants because MADE herself invisible.
It reminds me of something Oprah said in her Masterclass series. When she auditioned for the Color Purple and initially thought she wasn't going to get the role, she blamed her weight for the failure and went to a fat farm to shed the weight she thought had kept her from getting the role. While at the fat farm, she got a call from Steven Spielberg offering her the part and telling her that she better not lose any weight.
She believed that her weight was an obstacle, when in fact it wasn't. Her insecurity about her weight led her to blame her weight for losses (or presumed losses) in her life that were not in actual fact connected to her weight at all.
I believe that most of the women in this thread mean well, but I can't agree with these ridiculous over-generalizations that are mainly coming from single women about what most "quality" men want. A single woman (myself included) by definition hasn't yet managed to figure out what even one quality man wants, that's why she's still single.
So I'm not going to talk to you about catching a man. I'm trying to talk to you about catching yourself. You get one body in this life. Love that body. You get one soul, one spirit, treat it with kindness. You are not alone in your quest for love, and all of us questers are just trying to figure out the best way to get where we want to be, but like Oscar Wilde said, to love one's self is the beginning of a life-long romance.