Came late to this party, but agree with
@Gamisch. Also there is a factor that if you are embarassed to be seeing with such a girlfriend in public, or if people looks at you as a couple, or ask questions like, is the lady you are with your mother, etc..... or your folks/family/friends are in shock that you with someone that looks like her, then there are allot of negatives involved.
I of myself am not that picky in terms of looks when it comes to women, but as
@Gamisch pointed out, if that hb4 feels she is the best that I can get and I need her more than she needs me then that's a set-up for more disappointment, heartbreak and anger. You'll just inflate her ego, she'll think she can actually do better, and will treat you poorly and have one foot out the door the whole time.
A girlfriend and yourself should at least look somewhat "natural" together with you as a couple. People should not wonder if she is your mother, daughter, or what is the deal with you both together. Sometimes, you have less attention if you are by yourself then if you are with someone that doesn't look natural with you.