That sounds interesting, unfortunately I don't know of anything like that. A strategy (or even endgame) book would have good examples, but I don't know of any material that solely focuses on weak squares.
The basic idea though is a square that one player can't easily influence, but the other player can. Since pawns can chase out all the other pieces, generally a weak square is one that can't be defended by a pawn. Generally the way you exploit them is as infiltration points to attack surrounding squares.
For example in the diagram below, black is practically winning already. The c2, c4, and e4 squares are all weak squares, and make for good infiltration points for black's pieces. Getting a rook to c2, and/or knight to e4, c4 are all strong ideas for black.
On c2 a rook would pressure everything on white's 2nd rank. On c4 a knight would pressure the e3 and a3 pawns.
Does anyone know of any good training material (online or book) that focuses on weak squares? I would prefer a book that has questions or puzzles at the end of each chapter.
Thanks in advance