Datapoints from recent weeks: I flew BA15/BA16 to/from SIN with checked bags similar to yours (15kg and 27kg). As has always been the case in my experience, BA tagged the >23kg bag with the orange “Heavy Bag” label (which also has the text “Heavy Bag charge applies”). This was both at LHR and at SIN, but I expect it would be no different at SYD.

But as others have stated, if you do indeed have OWE status, then you will not be charged extra for the heavy bag.