To keep this from happening, you need to demonstrate some independence. Show that you have a life of your own. While you should keep the focus on her, when she talks about something in her life, you can briefly mention something in your life that is similar. If you do a variety of things in your life, it should be easy to appear independent. On the other hand, if you act like you are never too busy to drop everything to see her, and that as far as you are concerned there are no other women in the world, you will be seen as dependent.
Dependency is unattractive.
My female best buddy told me that she didn't like to answer this question because her view of attractiveness varied with every man she knows. She and I agree that attractiveness is not a receipe to follow. I maintain that the same holds true for men. One of the first things you need, Cash is handy if you want to go anywhere, but most wealthy guys are a lot more arrogant, domineering, and all-around stuck up jerks than your average guy. The fancier, the better.