One of the first and most common claims made by plaitiff's attorneys sueing for damages arising from airline mishaps is the aircraft was operated out of weight and balance.
It is a safe accusation to make long before the NTSB finishes their investigation. That is because passenger weight and carry on bag weight is estimated based on approved averages. Used to be even checked bags were based on an average weight. I don't know if that is still true. Bottom line. We never really know exactly what the aircraft weights, but it is FAA approved and never seems to be an operational issue.