But you need to put your systems somewhere. Hull mass is only increasing if you assume you only have hull. The space between the stabilizers and reactor is where all your chambers, shields, weapons, thrust, etc go.
I'm not sure if I'm getting your meaning exactly, but if for example you:
take a ship that is reactor, stabilisers at 100% SE, hull to cover the power systems, and then enough systems to consume all power (say just a big group of shields for argument's sake),
and then modify the ship:,
move the stabilisers closer to the reactor (there's still heaps of room for your shield group), add some more stabilisers to bring reactor output back up to max, then trim off all the hull now in front of the stabilisers.
After this modification your reactor is unchanged (and so is your power output), your stabiliser group has gotten bigger and heavier, your hull has gotten smaller and lighter, your shield group (systems) is unchanged (and is still consuming exactly 100% of the power produced, because power output is unchanged).
If we say that stabilisers became 100 mass heavier, and hull became 500 mass lighter, the total ship has become lighter by 400 mass - and if we did exactly the same experiment but without bothering to put the shields in we'd still see exactly the same result of the total ship getting 400 lighter.
Because the shield block stayed constant, it had no effect on the outcome, so it isn't necessary to actually put it in - we know it stays constant.
Possibly I've been confusing the issue a bit (apologies if so) because although the examples I post are ships with constant power getting lighter, I most often describe the mechanic as a ship with the same mass getting more power.
But these are logically equivalent (in SM at least), so it doesn't matter which way you say it (or show it).