Somewhere (probably on a BA.com page that someone will be able to find more easily than I will) I remember reading that the overweight fee is waived for the card holder ONLY.

As for the extra bag, I think that may be for all parties on a single booking, but I'm not sure.

In practice, I've never had to push the matter. I'm usually on a Club or First booking, so weight on the standard allowance for all passengers would be waived either way, and as of recently my travel companion is also Gold, so even he (an epic overpacker) has trouble getting close to the maximum baggage allowance!