Caroline thinks that Auntie Braxton and the Captain should marry because it is the practical thing to do. Auntie Braxton has been ill, and while she was in the hospital, the Captain had stayed at her house, as he had no place to live after his own house was ruined in a storm. Now that Auntie Braxton is getting out of the hospital, she is going to need someone to take care of her, and the Captain needs a place to stay. The Captain is fond of Trudy Braxton and is a skilled and gentle caregiver, but if he stays with Trudy when she comes back home, people will talk about them; in the staid, Puritan New England philosophy which is predominant in the area, it is not considered proper for a man and a woman to live in the same house if they are not married. Even though it is clear that the two would be living together as a matter of practicality and convenience only, they would be opening themselves up to the censure of the society. As Sara Louise says,
It's how it looks. People don't think it looks right for people who aren't married to live together in the same house."
To Caroline, the solution is simple - the Captain and Auntie Braxton should just get married. As she so logically reasons, Trudy Braxton
"needs someone to take care of her and her house, and (the Captain) need(s) a house to live in. It would be a marriage of convenience" (Chapter 13).