I think this is hit and miss.

I had my hand luggage weighed once when flying out of AMD (after passport control and before security).

Recently, I flew out of LHR and the check in agent noticed I had a laptop bag and suggested that I put it inside my hand luggage since my allowance was just 1 bag (I was in Y). I guess I've been used to the 2 x bags allowed in all cabins on BA with a 23kg allowance) and this is probably the one part I will miss about BA when I leave them following the recent changes.

Other than that, they've never weighed or checked my allowance on QR.