My brother-in-law has that very same set, and while it is very nice, the pieces aren't weighted at all.
I think piece weight is a matter of preference. I personally like wieghted pieces. I bought a cheap wooden set, and while being cheap it is at least double weighted and feels good in your hand. It feels good to move a weighted piece across the board. Plus, being weighted, there's less chance of accidentally knocking them over.
I think that Ambassador set is very nice and the woodwork on the folding board is awesome. However, if the pieces were weighted I think it would be better. I think it could be easily done by removing the felt, drilling a hole in each piece, filling it up with a mixture of birdshot and epoxy, then replacing with new felt. However, it's something I would want to be very careful about doing, and for an $80 set you'd think it would have been weighted.
I'm getting a chess set soon and this is currently 1 of 2 chess sets I'm looking at: http://www.chess.com/eq/chess+sets/ambassador-decorative-complete-chess-set2
I simply love the look of the pieces and board, but I'm not sure as to how it would feel without purchasing first. Chesshouse says the king is 1.2oz and the Staunton Championship set (other chess set I'm looking at) has a king of 2.1.
Do any of you consider weight when purchasing a new chess set & does it play any part in quality/longevity?