As to how it happens - weight may "accrete" on an air frame, as things like passenger wi-fi, or even flight systems, get added or upgraded (or even removed). And maybe not all departments "get the memo" of the change to aircraft N000SW's weight, so the records don't match. Big corporate bureaucracy (or perhaps too small and overworked a corporate bureaucracy).
Would it not make sense for the flight crew to complete their own weight and balance calculation using an EFB or similar device? This way the airline can ensure that they have up to date records of their own fleet weights without having to worry about disseminating the information to all of their handling agents and auditing it. The handling agent present a loading form with passenger weights, distribution and load in compartments for the flight crew to enter into their own EFB. Similar devices are used for computing takeoff performance, surely adding a WB function wouldn't be too difficult?