Originally Posted by Porosenok96
99% of the kids playing at chess tournaments have this set http://www.uscfsales.com/chess-sets...-pieces-vinyl-chessboard-deluxe-bag.html
You can get single-weighted, if you are afraid that this one is too heavy (and it probably is for a 6yo chess player).
Triple-weighted is good for small children, because they tend to knock things over. They will be strong enough to easily move the pieces. At a tournament, players are sitting at opposites sides of a table, and small children have trouble reaching the opposite side of the usual tournament-size board. A set for playing at home on the floor should probably be smaller.