Thanks for your reply Number_6, but I am still unclear about something. The benefits listed on the OW website depend on one's status on each airline. But what happens if you fly a different airline? Will that airline follow the rules of your programme or those of their own programme? If the former than they could end up treating their own elite members worse than others. VV could also happen.

In my case I am AA Plat and would like to fly CX from AKL-NRT but as I will be away for 6 weeks I really need to be able to take more than 20kgs (I will fly Y). Neither CX nor AA mentions anything on the OW website about additional allowance, but the CX website (Marco Polo) does.

If I can't take extra weight I guess my AA Plat card is not as useful as I had hoped. I'd have to stick with * for my flights this year.