When Yaakov saw Rachel daughter of Lavan his mother's brother, and the flock of Lavan his mother's brother, he rolled the stone off the mouth of the well, and watered the flock of Lavan his mother's brother. (29:10)
Yaakov's amazing feat (rolling the stone and watering all the animals - which normally would have taken several people working together) is quite surprising. It's romantic to say that he fell so strongly in love with Rachel at first sight that he was able to perform superhuman feats in order to impress her. But there is a better explanation, which in any case might be considered romantic too.
When growing up, Yaakov undoubtedly heard the story of how his parents met. Eliezer had gone to the well looking for God to deliver a girl with the degree of hospitality which would be appropriate for a future member of Avraham's family. All of a sudden Rivkah showed up. She was not only as hospitable as Eliezer could have imagined, but also beautiful and from Avraham's own family. Everything worked out perfectly, Rivkah agreed to the marriage, and she and Yitzchak lived happily ever after. It's the kind of story your kids would be embarrassed about, but it was such a good story that it merited a very long chapter in Tanach.
Note that Lavan is identified as "his mother's brother" three times in the one verse describing Yaakov's actions. The focus is not on Rachel, or even on Lavan, but rather on Yaakov's mother Rivkah. Just one thing is on Yaakov's mind, and that is his mother and the story of her marriage. Like Yaakov, Eliezer had once gone to Haran and stood by the well until a girl from Lavan's family showed up. That girl had shown extraordinary kindness to Eliezer, and now Yaakov plans to repay the favor. He draws water and waters Rachel's animals just as Rivkah had done for Eliezer so many years earlier. Later, Yaakov will fall in love with Rachel and marry her (it is touching that their relationship begins with this act of gratitude and generosity). But for the first few minutes, it really does not matter whether Rachel, or Leah, or a man had arrived at the well. Yaakov just wanted to do for Lavan's family what Lavan's family did for Eliezer, and Rachel was simply the first family member Yaakov met.
After Rachel gave birth to Yosef, Yaakov said to Lavan, "Release me and I will go to my place and land". (30:25)
Why does Yaakov choose this particular moment to ask Lavan for permission to leave?
This can be understood by looking at one aspect of the Torah's (or ancient society's?) understanding of family structure. A Jewish woman who marries a kohen is allowed to eat trumah (priestly tithe food), since she is considered part of his priestly family. After they get divorced or the kohen dies, she is no longer allowed to eat trumah, since she is no longer part of a priestly family. BUT, if this Jewish woman has a child from her marriage with the kohen, the woman is still considered to be part of the family along with her child, and can still eat trumah. (See mishnah Yevamot 9:5-6.) The upshot is that that women are considered potentially connected to their parents' households until they have children, at which point they becomes more permanently connected to their husbands' families.
Yaakov knew this when he made his request to Lavan. Rachel was the wife he loved and the most valuable person to him in the family. But as long as she had no kids, she was still considered connected to Lavan, and Lavan might find an excuse to take her away from him. Once Rachel had a son, this was not an option. She was now fundamentally part of Yaakov's family, and there was no conceivable excuse Lavan could use to prevent her from leaving with Yaakov.
"Your father swindled me and changed my wages ten times, but God would not let him harm me." (31:7)
Whether the phrase "aseret monim" should be translated as "ten times", or "tenfold", or "many times", or simply "exceedingly" is not my concern here. What matters for now is that Chazal understood it to mean "ten times".
The suggestion that Yaakov was cheated ten times parallels the midrash that Avraham underwent ten trials. What in fact is the source for the number ten in relation to Avraham? I suspect that it was derived by comparison with Yaakov. Each of the ten times that Lavan cheated him, Yaakov would have been tempted to do a little cheating of his own, to "even things out" and to recover the money which "really belonged to him anyway". But not once did Yaakov succumb to this urge. The ten times Yaakov was cheated were in effect ten tests, and each time Yaakov passed the test. Avraham, too, had been put in a number of difficult situations and each time had "passed the test" successfully. Noticing the parallel, Chazal fixed the number of Avraham's tests to be exactly ten, just like Yaakov.
The parallel between Chazal's conceptions of Avraham and Yaakov is clear, but there is also a big difference. Yaakov was involved in a number of complicated and morally confusing situations - with Esav, with his parents, and of course with Lavan - in which the right choice was neither obvious nor easy to make. In contrast, Avraham's tests were easy to understand, though painful to carry out. This difference is reflected in the roles Avraham and Yaakov play in Jewish history. Avraham's descendants include Yishmael, Esav, Ammon, Moav - nations which in light of Divine promises became numerous and powerful, but are not part of the Jewish people or God's plan for history. In contrast, Yaakov had many fewer descendants, but all of them became part of the Jewish people. The Jewish mission is not to be overpowering, heroic, and all-conquering, but rather to set a moral example for the world through observance of the Torah. Only Yaakov's trials, in which he was placed in confusing and seemingly minor situations which nevertheless had crucial moral significance, are sufficient qualification for this historical role.
(Perhaps related: God's revelations to Yaakov are not very revelatory; for example in 30:16-17 and 31:2-3 Divine intervention and revelation just confirm the natural order; whereas with Avraham, Divine commands repeatedly lead to unusual and unnatural outcomes.)