When is too much too much?

Is it possible to be TOO considerate? Or TOO friendly? How are you supposed to know if people are truly your friends or are just humouring you? Perhaps, merely tolerating you because they have nothing better to do at the moment. At what lengths should one attempt to go to reach out to someone in friendship?
I have a friend who calls me quite often. She tells me all about her family problems, the back breaking schedule that she keeps for herself and complains incessantly about, and about the great time she recently had with her best friend. We don't see each other very often because of her rigid overscheduled lifestyle. We got together fairly recently and it was exhausting. Not because we did anything athletic or exciting but because it was several hours of listening and trying to appear interested in her incessant chatter. It is nearly impossible to get a word in edgewise and quite impossible to get an entire sentence out before being interrupted, and having the topic swept back to her. I feel like the stand-in when her real friend is unavailable.

Obversely, there are a few people with whom I would like to spend some time getting to know better. These attempts often fail for whatever reason. Maybe I appear too needy, or exhibit stalkeresque traits. Perhaps the "killing gift" kicks in and people quietly slip away to change their phone numbers. Who knows.

I think it must take great skill in having a balanced friendship where one is not dominant over the other and where the people involved have actual two-sided conversations.