I feel like I am missing why the maximum load factor doesn't go up as the aircraft is lighter.
Mathematically, it does. But, there will not be any approved data to support operations into that corner of the envelope. The limiting G factors are prescribed by the design standards and regulation, not convenience to the pilot for pushing it.
If a pilot chooses to pull really close to the G limit on a decades old airplane, I hope that they know its airworthiness intimately!