Okay I think I can clarify this: Electrons trapped in the gate (when storing a 0) come from the substrate. The substrate is connected to ground, and the “lost” electrons are replenished. So yes, net chip weight grows when 0s are written.

However, weight relative to what? All 0s on a chip will be heavier (the heaviest). All 1s would be the lightest. 50/50 1s and 0s would be the middle, which is where I’d expect generic “data” to fall.