Well no, but aircraft are weighed to get the Basic Weight.
This is for an airline A320.
This is the weight of the aircraft ready for service. Toilets are serviced, water tank full, All the seats, galleys and equipement fitted, but no catering, and the fuel tanks empty. This is done every two or three years for every aircraft.
When I did it we used a set of scales, one for each undercarriage. The results are printed on a Basic weight and index table, which is fixed to the cockpit door.
Then you add the operating crew and their baggage, the catering, the passengers, baggage and freight to get the ZFW.
This has to be done an hour or two before departure, so that the flight plan can be prepared. This weight is called the EZFW (estimated). Using the EZFW, the computerised flight plan system can work out the fuel required, which is checked and agreed by the pilots.
Then the plane is readied for service. Hopefully the EZFW will be near enough! If the actual ZFW goes up, at a certain point the Flight Plan will become invalid, about 2 tonnes is allowed for a narrowbody, or 5 tonnes for a wide body before a new calculation has to be performed.
When the flight is closed after the standbys are given boarding passes, then the actual ZFW is calculated. If this is in limits then off you go.
Airlines operate hundreds of flights and get good at producing an EZFW that works.
We operate short haul, flights of around two hours. The ZFW is the factor that limits us, never TOW and rarely LDW. The tricky one for the dispatcher is the B763. Lots of freight in the fwd hold, and a nearly full load of pax and bags, can give you a ZFW limit, and especially a nose heavy CG. Quite common to close the flight and find you have exceeded the fwd CG limit, especially when there are few business class pax.. Then you have to move a couple of pax from front to back to balance the plane and close the flight.