The "free" baggage allowance is 23kgs per bag. Above this BA charge £30 per bag unless you are exempt which, by being in CW, you are ie you can take upto 32kgs without any additional charge. Note that even then the max a bag can weigh is 32kgs ie they will not accept a bag heavier than 32kgs
Weight of each bag:
Each bag over 23kgs (51lbs) and up to and including 32kgs (70lbs) will incur a charge of £30 ($50 for journeys from all US airports) at the airport.
This fee will be converted into the local currency during the check-in process.
The following customers are entitled to a 32kgs baggage allowance per bag at no additional charge:
Customers travelling to and from Brazil.
Gold and Silver Executive Club members.
First, Club World and Club Europe customers on all routes.