For a UuA from WT+ to CW you should be paying the difference in carrier surcharge. The carrier surcharge applicable is route specific, generally though the longer the route the more the surcharge. For example starting from the UK the additional surcharge for CW over WT+ for a return to NYC is around £106 so the cost of doing a UuA for a return should be 20k avios and £106, and 10k avios and £53 for a one way UuA.

For a UuA from CW to F there is no difference in carrier surchage or APD, so it will just cost you the avios required.

Y to WT+ UuA isn't very common as you need to be booked in the very expensive economy booking classes to do it (Y,B,H). From Y to WT+ there isn't any additional carrier surchage. There may be additional APD in some cases though if the leg you are trying to UuA is exUK and you aren't merely connecting in the UK. For example, the APD for a Y class return from LON-NYC is £69, whereas the APD for a WT+ class return on the same flights is £138. As the APD is payable for leaving the UK and not arriving, the extra APD would only be charged if you did a UuA from Y to WT+ on the outbound from the UK. If you just UuA the inbound back to the UK there is no extra APD to pay.

Also, in all cases any changes in taxes, charges for customs, immigration, YQ, airport service fee, passenger service charge which have happened since the original booking was made will be taken in to account. This should me minimal if not zero.

In all cases the extra avios to pay is the difference between the avios for the cabin you wish to upgrade to minus the avios for the cabin you made your booking in. For example one way avios to NYC would be 30k in WT+ and 40k in CW, so the extra avios due to do your UuA is 10k. There is a calculator here on the ba site to work out avios differences.