I will try to cut out most of my psycho babble bull$hit here.......
Women have this need for attention once you have given it to her, she plays on it basically. It isn't always about *attention* though. It is about acceptance. Back to the attention seeker aspect here, women seek attention to fulfill a thought of their self attributes and for someone,perhaps you,to do just that.
The girl that craves acceptance, is soley because she wants someone to like or love her more than she does herself. This is because she has never had anyone REALLY love her or LIKE her. She develops the mind frame of a fantasy world basically temporarily to indulge those cravings. She may not like her attitude, self image, or other materialistic things in her life. She meets a guy who is "different" and she will cling to him like a bounce sheet right out of a dryer. Because she feels "different" and craves to be with someone "different" than she has ever met in her life.
So, if a girl is into you that is more so the reasons why gentlemen; that when you get a girl that is "clingy", you bounce..(pun intended).