There is an APD difference between economy and business class on an exUK flight. APD on an economy longhaul to PHL is currently £69, whereas any higher class is £138. This difference is payable, so you should have been charged if you upgraded from economy to business - unless a term of the certificate is that US picks up this extra APD for you. There will probably have been a carrier surchage difference as well to pay.

For upgrades from WT+ to CW on BA (either using a GUF or with avios) there is no additional APD to pay on an exUK flight as you are already paying the higher rate in WT+, although there is extra carrier surcharge (around £53 for LHR-PHL).

Obvioulsy if you are transiting the UK in the scenario when no APD is due in economy, then there would still be no APD due in business class.