BA emails (e-ticket confirmation) says
Checked baggage Adults and children: 2 bags at 23kg (51lbs) per bag per passenger
You may be charged for extra or overweight bags. There are restrictions on what you may pack and on the dimensions of your bags.
> British Airways baggage information
> Baggage Charges
Different baggage charges and restrictions may apply on other airlines. Please see the operating airline's website for information.
> American Airlines
I tried with Twitter last night, they confirmed that 2 bags are allowed for my route, but they are not able to refund any bags fees, and I need to continue contacting Customer Relations.