There's an episode of 'Heathrow - Britain's Busiest Aeroport' in which at check-in the guy checks in the right weight (over-weight) to the loadmaster, but offers a discount on the overweight baggage charge, on a flight to either Pakistan or Bangladesh, I'd have to watch the episode again to remember which. The reasoning is that you get repeat business that way, whereas sticking adherently to the rules and charging for every gramme overweight might cause your pax to choose another airline next time.
Getting the aircraft loading is right is the job of the loadmaster, it affects the aircraft trim, and fuel load, the weight needs to reported correctly. But a bit of flexibility at check-in on *paying* for over-weight baggage can do wonders for passenger relations. I don't think BA understands this.