In "The Witch of Blackbird Pond", what actions of Nat Eaton make Kit want to marry him?

The plotline between Kit and Nat is one of those classic love stories when the characters initially don't like each other, but later grow fond and eventually marry.

Kit first meets Nathaniel Eaton aboard the Dolphin on her way to Wethersfield. Nat is the first mate and the captain's son, as the ship belongs to his father. He thinks Kit is arrogant and spoiled. She refers to the ship as "filthy," and Nat finds this offensive since the ship smells because the Eatons make a moral choice to transport horses instead of slaves.

When Kit jumps in the water to save Prudence's doll, Nat jumps in after her. He is furious when he jumps in the water to save Kit, only to find that she can swim. He feels foolish and is forced to wear wet clothes all day as he has soaked the only ones he owns during his attempted rescue.

Nat is the first person to warn Kit that "only the guilty ones stay afloat," referring to witch trials that took place during this time period.

Later, Nat's feelings toward Kit soften when he sees that she is a good friend to Hannah Tupper. Nat has been friends with Hannah since he was a boy and Hannah found him crying in the Meadow, similar to Kit. They become friends as they work together to thatch Hannah's roof.

Nat becomes jealous when he hears that Kit is going to marry William Ashby and he and some of his sailor friends put jack-o-lanterns in William's windows as a prank. This lands them in the stocks and Kit is distraught to see the townsfolk jeering and throwing apple cores at Nat.

Nat eventually comes to Kit's rescue when she is accused of being a witch by Goodwife Cruff. He brings Prudence, who reads out of the Bible and convinces Goodman Cruff and the town that Kit is not a witch and all charges are dropped.

Nat returns to Wethersfield with a new ship, his own, that he has named The Witch. He tells Kit about it and his hopes for their relationship, and Kit is eager to sail on her namesake, but Nat won't bring her aboard until she agrees to marry him.