If i am flying an intl flight landing in DFW and then transferring on a local flight to LAX, how does the baggage allowance work.

Example LHR->DFW (BA) in J.

Then i go through customs and i have to 'recheck' my bags, DFW->LAX (AA), but that leg is in economy.

What happens? Are my bags tagged by BA and i just drop them off at an AA counter.. or will they say you have too many bags and i have to then pay for the bags for the final leg of the flight?

Thanks!