Why does she care so much what I think? And what do I do about it?

(This paragraph is background information that may or may not be relevant, but I figured I'd better include it just in case): I met this girl a little over a year ago. We were both freshmen in college, living in the same building, seeing each other quite a lot. We became friends and soon, I started to have pretty strong feelings for her and eventually I fell in love. I courted her and courted her, asking her out and telling her how I felt multiple times over the year. The answer was always no, but her reasons varied each time (she wasn't over her ex, she doesn't date friends, etc). Regardless, after so much rejection I fell out of love with her (though to this day I still have feelings for her, just not as strongly) and now we're great friends. Nowadays we enjoy a pretty stable friendship with occasional flirting (though I'm not sure she realizes she's flirting, that's just kind of her personality) and what I like to think of as the dynamic of an old married couple (fun, harmless fights over stupid things). Of course, I'm not as good a friend to her as I maybe should be, but since I still have feelings, I'm afraid to get too close, or to make her think I still have feelings, because that would ruin the friendship entirely. My personal theory is that she does have feelings for me (though I'm obviously biased), but she has convinced herself so fully that getting together is a bad idea, the feelings might be entirely subconscious now.

Recently, she had a conversation with one of my friends where she told him, through streaming tears, how much she cared what I thought of her, and how incredibly important it was to her that I like and respect her as a person and a friend.

My question then is why? Why does she care so much what I, only one of her many friends (though admittedly one of her closest), think of her? I mean, everyone wants to be thought highly of and respected, but why does it matter so much to her? And why me? She knows I like her as a friend, and I've told her that more than once, so why is she still getting so worked up? Personally, I don't think anyone should have that much power over anyone else, and I certainly don't want it. Have any of you experienced this behavior before? Do you know why it happens or how to fix it?
Why does she care so much what I think? And what do I do about it?
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