AC 91-23A tells you more than than you'll need to know about weight & balance. I have a paper copy but couldn't find an electronic one at the FAA website.
There's more info in AC 43.13-1 & 2 - maybe there's guidance there on when the flight manual empty weight data needs to be updated.In Australia, once a series of logbook entries exceeds:
0.5% of max weight or 10 kg, whichever is greater
cg changes 2% of range or 5 mm whichever is greater
RPT and large twins require regular weighings.
I checked with the factory on the origignal empty weight of my 1979 Decathlon - back then they didn't weigh every new airplane - just took averages and weighed a proportion of new airplanes.
Regards,
Dave Pilkington