Even if the two flights are on the same ticket and you checked in for both together, 'compensation' for a weather delay really is just to get you to your destination safely. They may get you a hotel and/or food (required in Europe, almost never get it in the US) but they don't owe you anything else as vouchers, cash, upgrades, miles, or anything else.
As for the taxes, I don't know much about HK airport tax, but ask whoever you bought the ticket from would be my guess.
You can say it is weather delay. But CA has flight that can depart earlier, KA has no airplane in PEK the evening of the day before, which they should have done. They may have very flight delay and maybe they cancelled the flight from HKG to PEK and every passenger in HKG had gone home that night so they do not want to fly a empty aircraft to PEK to pick up the passenger in PEK in the next morning. Whose problem should this be?
I called CX the evening the day before depature and asked them if the flight in the next morning has any delay and was told everything looks fine. I asked this since I saw the storm that evening. I registered the cell phone notification for the departure time. I arrived at airport at 6:50 and was told the flight will be delayed to 11:30am. The notification comes to my cell phone on 10:30am saying that the flight has been delayed. Ridiculous, yes!