I understand how balanced 2nd stages work. I also understand how increasing the size of the diaphragm (and resulting lever length) present a mechanical advantage. But the two things are not related. A balanced 2nd stage still has to oppose IP, it just does so with a combination of IP and a small mechanical spring, instead of a large mechanical spring. Increasing or decreasing the size of the diaphragm has exactly the same effect on balanced and unbalanced poppets.
There are two performance advantages of balanced poppets; 1) Since IP is part of the opposing force keeping the valve closed, any changes in IP are mirrored and partially cancel each other out. This allows the 2nd stage to tolerate larger changes in IP without as noticeably changing cracking pressure. 2) Since IP drops during demand, so does part of the force closing the valve during inhalation. This 'should' result in lower effort to sustain inhalation, all other factors remaining equal.
I think the move to smaller diaphragms in more modern 2nd stages has to do with marketing and increased venturi assist, not balancing.