My personal theory is that Rey is Kylos little sister.
After Ben fell to the DS and slaughtered the Jedi Leia and Han (or maybe just Leia and Han never knew) hid Rey on Jakku so Kylo would not be able to corrupt his little sister.
This is truly the vibe I got all through the movie. I do not think she is a Kenobi or Lukes daughter (the first seems too far fetched and the later to trite and obvious).
In the now defunct EU Jacen and Jaina were twins and Jacen fell, while Jaina remained a Jedi and an amazing pilot. Rey obviously took to piloting very naturally the entire movie. The scene where Han offers her a job may have just been Han being Han but I prefer to think it was him trying to spend more time with his daughter. The scene where a First Order officer tells Kylo that BB-8 is on Jakku and with a girl, causing Kylo to whirl around makes me think he knows he has sister. Maybe he heard a rumor of another Solo child and has been looking for her for years. Also Kylos obsession with finding Rey, talking to her, taking off his helmet for her, offering to train her, I think he knows. Plus on the books there was an extra line of dialogue from the scene where Rey pulls the lightsaber from the snow instead of Kylo where he says, "It is you!"
Also near the end of the movie where Leia hugs Rey, I say that was a pretty motherly hug.
To explain a teary-Luke and Rey, Luke knows why she is there he HAD to have felt a disturbance in the Force when the Republic planets were blown up (just like Ben Kenobi on ANH) and he probably blames himself. After all, it was his failure to protect Ben from the Dark Side that caused Ben to become Kylo Ren. She represents all his failures, and the lives those failures cost, coming back and expecting MORE from him than hiding.
As far as Rey crying goes, after her visions when she first touched the lightsaber it is clear she has a strong connection to the Skywalker name. Probably during those visions she felt a lot of what Luke felt at the time; fear during the duel on Cloud City, the pain on losing his hand and learning about Vader, the hopelessness and shame he must have felt watching the Jedi Temple burn. She has a bond with him because of that.
What I am most curious about is whose grave Luke was standing by. He went into exile alone on that planet, so whatever is there he brought with him. It must have been someone important. Could be a memorial grave for his students, for Ben after he "died", maybe he just made it for Han. I don't know but there are a lot of possibilities.
Anyway, thats my Rey theory!!