While it will not affect OP's ticket, the "most generous" or "most significant" rules do not apply. Rather, the baggage allowance for the operating carrier of the first segment, applies to all segments. OP has an AA-marketed ticket (001-) and thus his allowance in J is 2 bags at 32 kg each. This wlll apply to the outbound trip as well as the return. This information should appear on his e-ticket receipt.