I like the use of the Weber-Fechner law, that's a lens I use to think of age as well :) The idea is that experienced time is proportional to log time, i.e. it's why time seems to move faster as we age. You could even measure your age in powers of two, like we do octaves.
Are you saying that a better way to measure perceived time is something like "1 year, 2 more years, 4 more years, 8 more years," starting from birth, and maybe call each of those increments a "log year"? I like it.
I guess the "natural" base to use to get the "right" number of increments is a pointless exercise, since it ultimately bottoms out in the question of "why is a regular year as long as it is?", but if we assume a base of 2, I'm currently in my 6th log year, and hope to die comfortably into my 7th. Actuarial odds are >80% in my favor.