on a RTW ticket, you can take check two peiced of luggage for each sector. The tricket states 2PC in the baggage allowance field. However, most airlines permit this as 2 x 32kg pieced. But AA changed their baggage policy last year and now limit all baggage pieces, whether on RTW ticket or not) to no more than 50lb (or about 23kg) or an additional fee of US$25 per piece is charged (up to 70lb).
AA is notorious for charging everyone the additional fee for bags between 50lb and 70lb. Even their most frequent fliers get charged this extra fee (its a fixed amount between 50lb and 70lb per piece).
Their excuse for introducing this limit was occupational health and safety for baggage handlers, but it is well recognised as another revenue opportunity since the same people will be lifting the bag even if it is 70lb with the fee paid by the passenger.
There are some exceptions, such as if your bags were checked-in on a non-AA flights (such as QF departing Australia) and are tagged through for a connection on AA, then you still need to collect the bags at LAX, clear customs etc and then place the bags for re-screening at the arrival point. As you are not checking-in the bags at that point, they are no re-weighed and no fe is charged.
But when you go to check-in at an AA desk for the next departure, you will be charged the fee.