JDiver

AA's baggage regulations are here. They detail how much baggage you can check in on various flights, with the variances for different countries (e.g. Brazil), and the exceptions that apply to some also can be accessed here.

In BA's case at MAN, they erred, as I understand it, because they should be charging in accordance with the IATA Resolution 302 (the rules applicable are those of the Most Significant Carrier, in this case AA,) and not their own interpretation as if you were flying BA alone. (And USDOT does not apply because destination, origin or furthest point were not in the USA.)

"BA me cobró £40 por mi exceso de equipaje, aunque deberían haber cobrado en acuerdo con la resolución 302 de la IATA, la tarifa efectiva de American Airlines, la aerolínea mas significativa en mi viaje, resultando en un cobro permitido de $30." (Assuming you purchased your ticket between August 30, 2011, and February 7, 2012; if prior to that, you were entitled two bags at no extra charge if they were within weight limits.)

Please see this thread for more complete information on IATA Resolution 302:

New interline baggage fee rules (IATA Reso 302): AA ontime adoption?

For South America to / from Japan, I'd reference:

There are folks who better understand these baggage regs than I do - check the thread referred to for further details.

(Quoted portions from aa.com Baggage page.)