It doesn’t replace regular mempool/relay – you still need some way to relay txs so that miners can apply PoW to them, and will usually want somewhere to store a backlog of txs, eg for cpfp/rbf purposes, for fee estimation, to see if someone’s paying you, etc.
It would only increase memory requirements for nodes by perhaps a few megabytes in the worst case – the idea is you only keep one or two weak blocks, and in the normal case most/all of the txs in the weak block will be in your mempool anyway. It might make sense to count the actual memory usage of the weak block store towards the maxmempool limit, though.