In The Witch of Blackbird Pond, what does Nat do to William's house?

Nat and his friends illuminated William’s house with jack-o-lanterns because he was jealous. 

Kit’s uncle tells her that William has been the victim of an “insulting prank.”  He tells her that William’s house has been “illuminated.” 

"You mean they burned it down?" gasped Rachel.

"No. They well might have. They put lanterns in the window frames that are waiting for the new panes. Lanterns made out of pumpkin heads, with candles inside, and unholy...

Nat and his friends illuminated William’s house with jack-o-lanterns because he was jealous. 

Kit’s uncle tells her that William has been the victim of an “insulting prank.”  He tells her that William’s house has been “illuminated.” 

"You mean they burned it down?" gasped Rachel.

"No. They well might have. They put lanterns in the window frames that are waiting for the new panes. Lanterns made out of pumpkin heads, with candles inside, and unholy faces cut in the sides to show the light." (Ch. 16) 

Kit finds this funny, even though the Puritans think it is horrible.  Her uncle calls jack-o-lanters the “devil's invention.” The three “ringleaders” are being held in a shed and will be put in the stocks on Lecture Day. 

Kit goes into town to see Nat in the stocks.  He tells her to get away, not wanting the townspeople to see her talking to him.  She doesn’t care. 

Deliberately Kit stepped closer. She marked the way the tight boards were chafing the hard brown wrists. "This is horrible, Nat!" she burst out. "I can't bear to see you in this hateful thing!" (Ch. 16) 

The incident is a turning point for Kit. She realizes that it is Nat that she cares about, and Nat cares about her.  He vandalized William Ashby’s house out of jealousy.  Nat realized that Kit did not belong with a man like William.  Beyond that, he had loved her from the beginning. 

Nat’s relationship with Kit was a complex one.  He was a free spirit, like she was.  He called her a tropical bird.  Kit married Nat, and was able to live an unconventional life but one that was more suited to her personality than the straight-laced Puritan lifestyle that William would have given her.  William might have been rich, but Nat was adventurous and that was what Kit preferred.