Hmm, I remember hearing that expression a couple of times. I like a good linguistic mystery, but a quick search reveals...confusion (and possible Hong Kong / Latin roots)!
AA制 was coined in Hong Kong, probably a couple of decades ago. It was in common use among Cantonese speakers in the Pearl River Delta more than a decade ago, and has since entered Mandarin, obviously to quite some degree to appear in a text book. The term's etymology is based on the concept of "I pay amount A and you pay amount A" (i.e. the same amount). In natural English, we would probably descride it as "you pay amount x and I'll pay amount x" (i.e. x = x).
the AA is latin, meaning each/every.
Symbol: aa, āa (of ingredients in pharmaceutical prescriptions) in equal quantities; of each.