I honestly think its all to do with how one comes across to people in general. I am short and fat, not at all attractive really, but do get asked out / chatted up fairly regularly (not necessarily by the men i really want, but not by awful people either). I am older than you, OP, and as I say, very VERY far from being a supermodel, and I never used to get chatted up at all. I was nervous, dowdy, frumpy, struggled with eye contact... I thought i was uninteresting and everyone believed me.
Then, I had a bit of an epiphany. I lost a fair bit of weight, changed the way i dressed, wore a bit more make-up, and made an effort to learn the names of two new people at work every day. I greeted people by name, smiled, laughed, looked them in the eye...and the way people treated me changed. They talked to me, they flirted a bit, and sometimes, they asked me out.
People believe what you tell them. If you tell them you are dull and have no redeeming features, and no reasonable person would want a relationship with you, they will believe you. Tell them that you are something a bit special (not in an arrogant way), that you are a happy, confident person who would be fun in a relationship, and they will believe that as well. Looks are far, far less important than attitude, but for me, knowing i looked nice gave me confidence.