As per IATA Resolution 302 you are entitled to a single baggage allowance throughout your itinerary. (I assume this was all booked on one ticket.)
In this case BA is your "most significant carrier" so the luggage allowance you recieve on your first transcontinental BA sector should(!) apply on all sectors. This should be automatically embedded into your ticket.
CX seem to know all about this since they have a webpage explaining it:
http://www.cathaypacific.com/cx/en_G...r-journey.html