If the bags are checked to final destination, in Asia, then the Most significant marketing carrier's allowance will apply which is BA at 3PC with a max of 32kg per item for someone with OW Emerald status
If the bags are checkedin to Hong Kong , then BA's allowances will apply to Hong Kong (3PC) and then CX's will apply onwards - which is 3PC max 60Kg for 1st class and 3 PX max 55Kg for business

You would then be liable for excess baggage for anything above 55kg/60kg at a rate ( for travel to TPE) of USD13 per kg - so 96 kg for an emerald status passenger would be $468 or $533 for sapphire

If this is on a through ticket, BA will check the bags from point of origin to TPE as long as there isn't a stop of > 24 hours in HKG

Note: if you are travelling on separate tickets, then the separate allowances will apply and you would be liable for excess baggage fees regardles

Have a look at https://www.cathaypacific.com/cx/en_...ier-rules.html which is pretty good at explaining mixed carrier allowances