One of the analogies which I use in training to hide the numbers (big numbers and, even worse, equations, often tend to frighten people who think that engineering is somehow related to beating your head against a brick wall) is to liken the wing to a rule (as in the office stationery measuring device around 12 inches typical length).
If you can bear imagining the situation without a picture .. it probably would help if you actually did the exercise with a rule .. and taking the simple situation where the problem is one of simple bending limits.....
If one holds the rule so that a central load can be applied downwards and tipwards loads up, then the situation is similar to a wing if one thinks of the central load as being the fuselage and the tipwards loads being the net of (wing lift - wing weight) where wing weight includes wing fuel.
For a constant fuel load, as we pull some G, or increase the fuselage weight (mass if you prefer), or some combination of the two, the extent of bending load necessarily increases and the rule deflects to form a nicely curved shape. Some basic structural analysis results show that the extent of bending is related to the maximum stresses experienced in the structure, so we are entitled to think in terms of more curvature = closer to the structural limits.
At some point, as the load/G increases and the bending increases, we reach a stage where enough is enough and any more curvature would cause an unacceptable risk of damage to the wing ... either static or fatigue.
Now, if we increase the quantity of fuel in the wings, maintaining all the other things constant, the additional fuel provides a mass, and hence force, downwards on each half wing ..... tending to flatten or straighten out the curvature. Now it is feasible to increase the fuselage load (i.e. more centre tank fuel) which, naturally, will increase the curvature of the rule.
If we consider a few different fuel weights it is not too difficult to see that the worst (i.e. most critical) case for allowable fuselage load will occur with no wing fuel load... hence MZFW. As it would be a bit difficult to schedule a sensible way of making use of these effects, the certification rules simply look at the worst case and we end up with a single figure for MZFW.
The same logic applies to the various freighter recertifications which trade mandatory outboard wing fuel against an increase in MZFW. This is one way in which a benefit can be obtained. However the exercise is an expensive and involved one as it involves a recertification of the aircraft .... we have all heard the old joke that certification only occurs when the substantiating paperwork weighs considerably more than the aircraft.
Similarly, the manufacturer can gain a structural fatigue benefit by following the same principles ... load the wings first, then the centre fuselage tank and fuselage aux tanks .... and use the fuel in the reverse order.