I know that the B767 and B747 are able to have increases and decreases to "structural" weights by writing a note in the AFM and paying a fee to Boeing.
My lot "lightened" their B762s a few years ago to lower the airways/landing charges in the domestic ops. Our newer B744s have MLW approx 10 tonnes lighter than the rest of the fleet.
Over the last 20 years or so, the "structural" weights of the B742 and B743 fleets were upped with minimal mods - new flap load relief computer etc.