Each block of the Iwahori-Hecke algebra of type A is determined by its core and its weight. In particular, to each partition of an integer we can associate its core and its weight. In higher levels (for Ariki–Koike algebras), the situation is more complicated, however we still have a notion of weight for multipartitions, as defined by Fayers. We will show how to naturally generalise this definition so that the set of blocks of the Iwahori-Hecke algebra of type A is exactly a superlevel set for this generalised weight function. In higher levels (for the Ariki-Koike algebra), using Fayers’ notion of core blocks, we will see that this fact is “asymptotically” true. More precisely, if the generalised weight function is large enough then it always corresponds to a block.