Translation:My brother-in-law read books all Saturday.
A good question. It's because a preposition (perhaps "dum" [during]) has been removed and since there can't be two subjects, the adjective and noun in the prepositional phrase pick up the "n" ending. "Mia bofrato legis librojn dum la tuta sabato." Why is that? Grammatically, I have no idea, but I know that's how it's done.