I think Brooke raises an interesting point, that this teen would prefer to be at your house rather than in her own home. And I'd add that so many of us have had trouble finding a babysitter because teens are involved with their own friends and with activities. So why isn't this teen?
Your friends have made other suggestions which haven't worked, but you don't say what those are.
If you rule out that there's something going on (and I actually don't know how you do that), then you have to stop with the hints. "Susie, I have suggested to you on over 20 occasions that stopping by so frequently and then staying for hours is a problem for our family." (Optional: "Frankly, I'm quite surprised that you don't have other interests, whether it's friends your own age or activities. Is there a reason for this that you'd like to share with me?")
Then I'd lay down the law: "One of the most important qualities in a reliable babysitter is knowing that my instructions will be followed. I'm very concerned that you continue to do what you want, and that you are not listening to me. That makes me worried about leaving you alone with my children when I'm not home. Now, maybe I've done too much hinting and not enough direct explaining, so I'm changing that now. Here is my family rule: children need to play alone and with each other, and not have an older person directing their play all the time. It is not convenient for you to be over here so often, and I need you to respect that. I expect my decisions and rules to be followed. You're not doing that. I don't want to end our babysitting arrangement, but I will if things don't change immediately. From now on, you are not to just drop over, even for a few minutes. We have a routine here and I want to follow it. Will you agree to this, or not?"
Then be prepared to find another babysitter, even if it means driving to pick up/drop off.
Maybe this teen is lacking in social skills with her peers, and she feels more secure with young kids. Maybe her social inadequacies affect her peer relationships. Kids on the autism spectrum, for example, often do not read social cues at all well. Perhaps that's going on.
And if there's something more sinister going on at her home where she's not allowed to do things with peers, or worse, that she's escaping something to the safety of your home, you (and she) have bigger problems. You can't tell what's going on behind closed doors, so even if her parents seem nice to you, that doesn't mean it's lovely over there.