With the weight system you're given a maximum you can check in without any restrictions placed on the number of pieces. So if your checked baggage allowance was say 60kg, under the weight system you could do 2 x 30kg, 6 x 10kg, even 60 x 1kg (!) and any combination thereof and you'd be fine, so long as the total checked weight did not exceed 60kg. Under the piece system (such as BA) you'd be constrained by both the number of pieces allowed as well as the maximum weight prescribed per piece.