If you are planning a similar (Economy in one direction and Premium Economy in the other) trip in the future and are traveling to a U.S. destination served by AA nonstops, consider booking the Economy leg on AA as a BA codeshare. You will not only get the free checked baggage, but you would also get to select Main Cabin Extra (extra-leg-room) seats with 35" or 36" of pitch for free, based on your BAEC Gold status.