The MZFW is a structural limit. It cannot be exceeded.
On some aircraft types, like the 747, a sized MZFW exists for most operational situations and a tapered reduced MZFW under a set of conditions.
Usually you will see such an increase in MZFW can only occur if another weight variable has been eliminated from use, such as an optional weight (fuel cell) at the extreme end of the weight arm of the aircraft, furthest away from the CG in other words. Thus if such (holds/tanks) are used the MZFW reduces.
Reason for this can be varied, but are mostly to do with the aircraft starting to get to the envelope edge of its controllability.
In reference to fuel cells, care is to be taken when using the auxiliary fuel cells as a problem may arise in the supply to the centre tank, thus potentially ending up with dead weight in a part of the fuselage. This may be the reason for MZFW reduction when a certain amount of fuel is used there. Alternatively it may be due to the use of a second optional auxiliary tank which is installed occasionally.