Thanks for all the responses, particularly those from John Farley and John Tullamarine which uncovered a number of aspects that I had not considered.
My interest stems from recent experience with a light twin. A reweighing revealed not just a substantial weight gain (almost at the level where I would suspect the previous documentation of being fraudulent) but also a substantial forward movement of the C of G, despite a load of new equipment in the tailcone!
We're now operating on the forward limit of the C of G, and I'm concerned about the consequences of leaving my kneeboard on the glareshield during flight, and issues like the need for longer legs.
What sort of tolerances are built in to the certification process limits?