Why did Kit believe "she knew already what she would see" on the day of public punishment in The Witch of Blackbird Pond?
Kit believes that she will find Nat and his shipmates in the stocks.
When she learns about the jack-o-lanterns, Kit believes that she will find Nat in the stocks on the day of the public punishment. She feels terrible about Nat, and decides to go to see him despite the possible damage to her reputation.
Kit is told that three men “illuminated” William’s house, and that they are being held for punishment. She is also told what the punishment is.
"Little enough, since we have a constable who is quick to his duty. The three ringleaders are cooling their heels now in his shed, and on Lecture Day they will sit for all to see in the town stocks." (Ch. 16)
Even though she is only told that the three men are “a rowdy band of rivermen from a trading ship,” Kit thinks that one of them will be Nat.
It did no good to remind herself that there were dozens of trading ships on the river, and that the Dolphin might well be out to sea by now. Kit had no doubt at all who one at least of the culprits in the stocks would be, and neither, by the smug set of her pretty lips, had Judith. (Ch. 16)
Kit knows that Nat is playful, has no love for Wethersfield, and has a thing for her. It makes perfect sense that he would play a trick on her suitor, focusing on the one thing that William has that he doesn’t—a house. His was a harmless prank, although the people of Wethersfield no doubt do not see it that way, and designed to send a message to Kit. William is stodgy and boring, and Nat is interesting.
When Nat found out that William was building a house for Kit, he was obviously upset. He confronted Kit about it, and although she tried to tell him that there was nothing definite planned, Nat was correct in reminding her that building her a house was pretty definite.
"An interesting cargo we had this trip. One item in particular. Sixteen diamond-paned windows ordered from England by one William Ashby. They say he's building a house for his bride. A hoity-toity young lady from Barbados, I hear, and the best is none too good for her. No oiled paper in her windows, no indeed!" (Ch. 14)
Nat is obviously hung up on Kit. He does not feel that marrying William is in her best interest. He also thought that they had an understanding. They both take care of Hannah. They both are outsiders. He feels hurt and confused that she would not mention this to him. It seems like she is settling, choosing the rich man with the advantages.
The incident with the jack-o-lanterns is a turning point in Nat and Kit’s relationship. She has had a difficult decision in choosing a man, and although she does not approve of what he has done, she feels sorry for him. Responding with “half pity and half annoyance” (Ch. 15), she realizes on some level that he is doing what men do—making a fool of himself for the woman he loves. Nat’s banishment from Wethersfield upsets her, and she feels embarrassed because everyone in town now knows about her friendship with Nat. Sooner or later, Kit will have to make a choice.