Ouch, Gemac is correct, you pretty much built this itinerary in the only way where they can charge you.
I'll try to break it down this way.

AA Sectors(LAX-SFO)
You and the other elite (OW Sapphire) get 2x23kg
The other 2 have to paid baggage fees

CX Sectors (SFO-HKG-TPE)
You (CX Gold) get 3x23kg
The other elite (OW Sapphire) gets 2x23kg unless he's also a CX MPC Gold
The last 2 get 2x23kg

So you would get 4 bags free on the AA sectors and 8 bags on CX. AA might decide to waive it for you, no guarantees though.
If you do have 5-8 bags, it might be worth it to LFBU (Load Factor Based Upgrade, search is your friend here)your LAX-SFO flight to get more bags free. In the end, you would end up paying 20 bucks for the 1 hr F class seat.

That being said, I would still short check the bag if you have >2hrs on your connection
(I do for most AA>CX connections)
1) To ensure that your bags are coming with you to Asia
2) And to ensure your bags will have the CX priority tags, CX does do a decent job on priority bags and they usually would extend it to your travel companions even on separate tickets.