It looks like you would be OK if you had a through booking, so BA's allowances apply. Cathay's website makes explicit reference to MSC on their website. Where you are looking is often wrong, look at the wider website rather than MMB (or check here!).

However you were right to double check. Cathay's baggage allowance is fairly feeble (unless going to USA, Qatar or NZ) and a eye-watering US$60 per additional kilo, for something like UK to HK. So in WTP in BA you are allowed 2 bags, 46 kgs, CX in Premium Economy - where available - is only 25 kgs (but an unlimited number of bags, it's purely weight with them).