I read a book recently - "He's just not that into to you".. insightful YES, harsh TOTALLY.
All that Jesse was missing is having someone to talk to.. I would put money on him contacting you every time that him and Rachel have a fight, break up etc. He just doesn't want to be alone and knows that you will be there for him (as you recently proved). Don't be anyones "second choice". He treated you terribly and you deserve better.. plus he doesn't deserve your friendship and if he was a worthy person he would know that!
Take care of yourself and let the past become the past xxx