How does British Airways permit a 23 kg bag in hand baggage? The carry-on baggage policy on British Airways states that:


  Maximum weight per bag is up to 23 kg (51lbs).


Two passengers, with bags near the weight limit could easily go well over 40 kg. And then there will be a few smaller laptop bags etc. inevitably stuffed into the overhead compartment, I imagine it can touch 50 kg.

However, the overhead compartments themselves have a stated limit of 32 kg. Isn't this an unsafe practice? If so, how is British Airways permitted to do so, and if not, why do other airlines not follow the same practice?
Easyjet has no firm weight limit and advertises this fact. From the website


  There’s no weight restriction for cabin baggage, as long as you can place and retrieve the cabin bag safely in the overhead lockers without assistance.


They also use vague language like “within reason” or “lift comfortably” but most people probably won't have 20 kg with them. Given the limited size of cabin luggage, you would need to deliberately carry dense, heavy stuff to reach that weight (books maybe? wine bottles and other liquids are off-limits and if you don't want to check in any bag you still need space for your other things).

And then, comes this (from the BA website you mentioned):


  Occasionally we may not have space to stow all hand baggage safely on board and you may be asked to check in some or all of your hand baggage at the boarding gate.


Bottom line: Airlines don't need to rely on a prespecified weight limit at all. They rely on the size restrictions and general common sense to keep things manageable and if it somehow does not work out, they can always gate check a few bags.