
You are a good friend/person for not wanting to take advantage of her. I agree that when you always pay others ways, there is a possibility that some of your friends could be motivated by the free stuff. Of course, the way she could test this would be to see how many people stick around when she stops paying. I have a friend who invites me to things and pays. I feel like it would be rude to refuse so instead, I try to do the same periodically. I really do think it puts less pressure on a friendship when everyone just pays their own way.
While your observations about her may be correct--it is her choice how she spends her money. Do you enjoy being with her? If you do, then giving her your geniune attention might really help her feel less secure. On the other hand, if you do not enjoy being with her, I am not sure if true friendship can be forced.
So maybe just enjoy your time with her and continue to offer to pay for yourself?