No single bag can exceed 32kg due to health and safety regulations for baggage handlers.
You can purchase extra bags at the check-in desk, but be aware that airport prices are significantly higher than online rates.
BA uses a dynamic pricing model, meaning the cost depends on your route, cabin class, and how far in advance you buy. Purchase Timing Price Characteristic Lowest rates; often discounted compared to the airport. At the Airport
Silver and Gold members (and Oneworld equivalents) often get an additional free checked bag on most routes, regardless of fare class (excluding Basic).