You are allowed a checked bag of 23 kgs, as per your e-ticket (and the general allowance for BA codeshared flights on Aer Lingus).

The cabin baggage rules, well Aer Lingus are reasonably relaxed about this and don't systematically weigh cabin bags. But if you take around 10 kgs in one bag and a small bag item then you would be fine. I'm putting it like this since I can't quite work out what you want to do, but don't read up on Aer Lingus' ticketing policies and pre-payment options, you have a BA ticket so these options don't apply.