As said above the write down to 1999 Kg is just a way of avoiding the eurocharges.
The removal of the placards and replacement of them with the placards stating the new operating limits would be required as would the replacement of the flight manual with one that reflects the change in the operating limits.
I see no reason to re-weigh the aircraft as the changes are all paperwork and no meaningfull physical change has taken pace to require the aircraft to be weighed.