What are some textual examples of societal expectations for marriage in Jane Austen's Emma?

The social expectation in Emma is that women will marry. Anything else is unacceptable. Women are also expected to marry a person of their own class.
Harriet shows how unacceptable it is for a woman not to marry when she expresses deep shock at Emma's declaration that she will never marry. To be an old maid like Miss Bates is, to Harriet, a terrible fate. Emma actually agrees with her, saying it is ridiculous to be unmarried and poor, but that she, Emma, will be an unmarried older woman with money, so people will fear and respect her. But in the end, threatened with spinsterhood when she finds out the Jane Fairfax is marrying Frank and when she fears Mr. Knightley will marry Harriet, she wants desperately to marry Mr. Knightley herself. Partly this is recognition of her love for him, but it is also evidence of her acceptance that marriage really is the only path for a woman.
In the beginning of the novel, much of the laugh-out-loud comedy can be lost on a modern audience: Mr. Woodhouse's repeated pity and mourning that "poor Miss Taylor" is marrying is the equivalent of someone mourning that a friend won the lottery or had an unexpected inheritance and is moving to a mansion in Palm Beach. For a governess like Miss Taylor to make such a good marriage is an amazing windfall, not something to mourn.
Nearer to the end of the novel, Jane Fairfax's seemingly inevitable fate of becoming a governess is universally pitied. To become a governess rather than marry is to fall down the social ladder, to "sink." Jane herself compares it to slavery. When her secret engagement to marry Frank becomes public, her status is enhanced and secured.
Much of the plot surrounding Harriet's marriage revolves around class expectations. She is illegitimate and doesn't have money, yet Emma can't tolerate the idea of her marrying Mr. Martin, a farmer. Mr. Knightley, however, insists it is a good match for Harriet, the best she can expect. We see through Harriet how much birth and money determine expectations about the person one will marry. That is the case too with Jane Fairfax—nobody expects that a poor, powerless (though accomplished and beautiful) woman like her could marry Frank Churchill—though in this case, as in "poor Miss Taylor's," she is able to marry well.