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).
You definitely don't need something more expensive now, but later, if you'll decide to go to a tournament, you'll have to invest in a good chess clock.

My ds7 plays in tournaments and got one that looks like this for his 6th birthday from a friend who also plays in tournaments. The pieces aren't heavy so maybe it's not this exact one. I definitely recommend getting one like this with a bag and board that rolls up. I also recommend chess clubs and tournaments. Great fun for a chess player!