What set does this large sand green roof piece belong to and what is it?
This part is Tower Roof W. Tiles and because its only made in 3 colors and as the other two available colors are black and lilac, this must be the sand green version. Color in the photo has a more blueish tint to it 

This version is only used in two Harry Potter Hogwarts set:

4842-1: Hogwarts Castle



4867-1: Hogwarts