In Sentence 5, what does the word “obliged” imply?

To understand the meaning of this word, we have to read the entire sentence. Earlier in the passage, we've seen that the two sisters were predicted to marry well; now, we learn that "Miss Ward, at the end of half a dozen years, found herself obliged to be attached to the Rev. Mr. Norris, a friend of her brother-in-law, with scarcely any private fortune, and Miss Frances fared yet worse." Based on their high expectations and dismal outcomes, we can see that "obliged" conveys a sense of resignation (although not actual coercion).