I assume you are on separate tickets and so not strictly connecting.

BA will be able to check bags through to another oneworld carrier, but should only do so within the allowance for that carrier/ticket.

CX generally operates on a weight system, not piece. If you are flying CX in J as a oneworld Emerald you should get a 50kg allowance, so can take 4 bags if they weigh under 50kg combined. It would be $10/kg extra.
http://www.cathaypacific.com/cx/en_G...ge-charge.html