What is the purpose of AY's 8kg limit on cabin baggage?
...
Your guess is as good as anyone's.
...
For the same size limit, why is AY's weight limit one third of BA's?
Imposing size limits makes a lot of sense, because there is limited space in the overhead lockers. But there is no more sense in imposing a low weight limit on cabin baggage than there is in imposing a weight limit on passengers' bodies or the contents of passengers' pockets.
...
I am pretty sure there is a load limit for the overhead stowage, and that is it way below a number allowing all bags to be anywhere near 23Kg. I don't know the exact load limit, but I have a vague memory of 39Kg per overhead section in a A320. You can fit several 56x45x25cm bags into there and so restricting each bag to 8Kg can be driven by a calculation on how many bags one section of the "weakest" aircraft cabin in the fleet can hold.
One can also make the case that a bag with unrestricted weight falling down will cause a lot more damage than a weight restricted bag does. Falling down does not only happen in extreme weather, but also from clumsy or weak passengers. If you ever been in a C or D seat when someone drops a bag on you, you might be happy it was weight restricted.
Finally, one can make a case for restricting weight in order to drive ancillary revenue. If you allow 23Kg bags, very few people have a need for a checked bag. With the trend of light (HBO) tickets I guess many airlines hope for revenue from passengers who has to purchase extra bag allowance.