You can have a heavier bag but you need to pay for the privilege and for the extra fuel comsumption. The company needs to attempt make a profit after all.

Heavier bags are allowed for BA Gold card holders but then these pax have previously spent a lot of money travelling with BA.

Having said that, BA does allow a 23 kg hand luggage (provided you keep within the right bag dimensions). Now that is very generous compared with any other airline I know of. However you will need to lift the bag by yourself on the overhead lockers or push it under the seat in front. The crew will not do this for you.