I'm pretty sure the OPs extra £120 is the higher fuel surcharge for CW over WT+ for the return flights.

I did a mini-analysis on an envelope for a long-haul single sector the other day. The fuel surcharges were: WT £239, WT+ £276, CW £359.

Very crudely BA are implying a CW passenger takes up 50% more weight all-told. I tried, honestly I really tried , to look at this.

I would believe the CW seat is significantly heavier than the WT equivalent but could find no real data on this.
I do believe the average CW passenger carries more check-in than the average WT (35kg to 22kg on my estimates, which recognises a lot of Gold and Silver travel WT).
I didn't find much else where fuel burn would be different.

The funny thing is: I came up with the average WT weight-load being 112kg + the WT seat; vs. average CW at 127kg + the CW seat. We'd be talking 10kg and 50kg seats to make BA's sums right; which doesn't seem so unbelievable.

Disclaimer: The above is merely on an envelope, it is not claimed as fact