There are two dimensions to baggage, weight and volume. The piece concept restricts the volume that can be carried as well as the weight.

With a weight concept you can potentially check in very large, very empty cases which take up a large amount of space in the aircraft's hold and if enough passengers do this then it may be necessary to offload bags, which leads to a number of costs.

Accordingly by offering a piece concept BA can ensure that there is space for cargo AND offer a higher total effective weight allowance for premium customers.