From BA.com
Information for frequent flyers
The following frequent flyer members can check, free of charge, an additional bag regardless of their class of travel (except hand baggage only fares). This applies to all customers travelling on the same booking (excluding special group rate bookings).
British Airways Executive Club Gold
oneworld Emerald
The following frequent flyer members can check in two bags in all cabins, on all routes, unless the cabin allowance is greater (except hand baggage only fares). This applies to all customers travelling on the same booking (excluding special group rate bookings).
British Airways Executive Club Silver
oneworld Sapphire
The following frequent flyer members can take the maximum weight of 32kg per bag without paying the heavy bag charge. This applies to all customers travelling on the same booking (excluding special group rate bookings).
British Airways Executive Club Gold and Silver members
oneworld Emerald and Sapphire
Best to print out this as the CSO sometimes r not switched on and not aware of the rules.