Welcome to Flyertalk and welcome to the BA forum.
I think the MSC stuff is a red herring. Unless I am much mistaken, your original booking with BA had 1 bag with 23 kgs, and that should be honoured by QR (and generally it is, by the way). If you had already paid for additional bags then they too should carry over. If you end up out of pocket, compared to your original booking, then just claim the excess from BA, they normally just pay up. It's not that unusual. This includes any bags over 23 kgs, and based on the delta between QR and BA.