Years ago when flying with ExCalibur on the A320 we were getting check gross weight messages on the FMGC and the fuel burn was a few % above the book.
We were using assumed weights for hold baggage so we decided to start weighing the hold baggage (and incidentally on flight to FNC we weighed cabin bags too). This showed we were often heavier than we had previously thought. We never got anymore FMGC messages and the fuel burns were almost exactly as advertised.
As and aside it seems quite amazing in this day and age of modern technology that we do not have an accurate system on the aircraft which tells us what the actual weight is and where the c.g. is located.