There is a general point to make here that one of the few advantages of codeshares is that on paper the checked allowances for BA continue on the other airline (with some uncertainties on anything extra you get from BAEC status), so despite Aer Lingus having a complex web of checked luggage allowances, for BA it's 1 bag x 23 kgs, or 2 bags in business. So that's straightforward and the e-ticket can be relied on since that's what the agent will see at check-in.

But cabin luggage protocols are different, and can vary from 6 kgs to 23 kgs on different airlines. Plus Aer Lingus' regional services simply don't have space for big items on their smaller aircraft. So yes the general rule is that checked luggage broadly follows BA's logic, cabin luggage is more complex. But as I say so long as you don't overdo it, Aer Lingus are reasonably relaxed about this, particularly on Airbus services.