After a particularly lucky break where he rescues two lost women who happens to be quite wealthy, Tevye collects enough money to stop wood cutting and open a dairy business. Cue a whole new set of worries. Now he's less concerned with feeding his daughters and more worried about getting them suitably married off.
With the dairy business, Tevye feels like "a wealthy man [who goes out] every morning to the market" (2.2). Now that Tevye has risen (slightly) in the world, he needs to collect enough money to provide dowries for his daughters. His idea? To invest in the stock market with his cousin, which, not surprisingly, does not work out well. This means that it'll be hard for the girls to marry anyone in their socio-economic bracket, leaving only husbands too rich to care or husbands who don't mind staying poor.
Despite Tevye's best-laid plans to get her married to a wealthy but "somewhat common" (4.34) butcher (ooh, burn), Tzeitl marries a poor tailor and she ends up very happy. This sets up the family precedent for love-based rather than arranged marriages. Hodl's marriage is similar to Tzeitl's: she marries a member of a revolutionary group who promptly gets himself imprisoned and exiled. She chooses to go with him and sends back happy-sounding letters. Overall, we get the sense that Tevye is okay with breaking the arranged-marriage tradition.
Love turns out not to be all you need, when Chava falls in love with a non-Jew, runs away from home, and hides out at a priest's house. In response, Tevye disowns her and refuses to even acknowledge her in the street. Meanwhile, during a wave of pogroms against Jewish villages, Shprintze gets engaged to a wealthy young man. His family is not so thrilled, and she drowns herself.
Learning from these examples, Beilke agrees to an arranged marriage with a wealthy contractor, with the practical if somewhat depressing idea that this will help her family financially. Hey, we said dark, didn't we?
Beilke's husband goes bust, Tzeitl's husband dies, and just like that, the non-Jews of Tevye's village are at his door demanding to beat him up and wreck his house, as per government instructions. This sets up what will be the final philosophical idea of the stories—that Jews can't count on being accepted even in a place where they've seemingly acclimated and assimilated.
Although he uses his smarts to convince the villagers to only break his house enough to make it look good to the authorities, Tevye has no ammunition to use against the government itself. Which is too bad, because the government has just made the village into a town and ordered out all Jews. (Oh, yeah, and seized their property.) Packing to make their escape, Tzeitl tells Tevye that they can't leave Chava… who turns out to be in the next room, bags packed and ready to go.
Tevye forgives Chava, since she's returned willingly. As they head out, he thinks about the fact that assimilation is not a valid solution for Jews, since they remain unaccepted by others. Instead, he throws out the suggestion of a geographical location where all Jews could live and belong.