The first important piece to consider when interpreting or analyzing this piece of art is remembering that this story, although fictional, did correspond to an actual controversy that happened in 18th century New England in which a neighbor of the author of the novel impregnated his mistress who then killed herself from the shame and confusion.
Brown's attempt to fictionalize the story was likely an expositional attempt to address the confusion that the affair meant for his community. A few dominant themes arise that help to bring his point more to the forefront.
The first is that social decorum is not just for fashion's sake. In the novel, if the relationship had been done according to custom, in the light so to speak, then the incestuous nature of the relationship could have been brought to the couple in private to avoid shame and guilt.
The other is about shame itself. This is not emphasized intentionally, but American culture is so different than it was then that it merits mentioning: To do something inappropriate was not just frowned upon. It was grounds for death or ostracism. The suicides in the book are likely not just a response to the internal fret brought on by the couple, but also an intelligent response to the harsh reality that awaited them for the rest of their life.