I just copied/paste this off the BA web site. It seems to me that you can have a suitcase weighing 23 kg for the hold and hand luggage weighing 23kg but it can't be larger than laptop/handbag/briefcase. So the size of the latter will restrict the weight unless you've got a lump of lead in it
The following allowances apply for all passengers entering the UK or departing from London Heathrow, London Gatwick, London City, Aberdeen, Edinburgh, Glasgow, Jersey, Manchester and Newcastle:
one standard-sized bag - maximum size of the bag must not exceed 56x45x25cm (22x17.5x9.85in) (including wheels, pockets and handles)
In addition, one laptop sized bag, handbag or briefcase
A 23kg(51lbs) maximum bag weight applies and you must be able to lift the bag into the overhead lockers in the aircraft cabin unaided.
NB. Cabin crew will assist customers with additional needs.