BA website clearly states how much each of your carry on bags may weigh, depending on cabin flown. However, as is typical with ground staff, how strictly this is enforced depends on which agent checks you in. At ORD, it is not monitored like it is at LHR. And at LHR, I have been told to re-pack my two carry ons by a surly agent such that each bag weighed the precise amount, even though the total weight did not exceed the limits . . . and I was in J !