There's also that practical point which is that you could be in bed in the Sofitel (or having breakfast in the Arrivals lounge if you qualify) rather than queuing up at the carousel and then lugging bags around. You'll have boarding passes for the BUD leg so don't need to recheck bags or queue for a desk, you should be able just to go to security.

I wouldn't even contemplate trying a short check in this situation. The BA hand baggage allowance is generous anyway so you can get a max size bag which is enough for a week. So mix and match what you need during the layover and to cover the low probability of the bag not making it.