Littlefinger knew that the northernmen are loyal and will only follow a Stark, and the only living Stark is Sansa who will inherit Winterfell ( because everyone else thinks that Bran,Arya and Rickon are dead). He thought that if he helped Sansa in regaining Winterfell and avenge the Red Wedding by killing Ramsay (as he was the last Bolton), he would able to persuade Sansa to help him in the war against the Lannisters and crown him the King and Ofcourse later he can marry her.
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