IMO, only good reason the Merlin Mustangs gained weight was the two stage Merlin was about 300 lbs heavier than a single stage one or an Allison. The development of the lightweight Mustangs IMO is proof that Schmued knew that the P-51 was overbuilt. Not to mention that even when armed the XP-51F and G models were lighter than the NA-73X, and still had decent range on internal fuel (not as good as the B/C/D/K or even H, but still way better than a normal spec Spitfire).
Even the Rolls-Royce FTB Mustang with a Merlin was a good deal lighter than a normal Merlin P-51 (max take off weight estimated at 8950 lbs for the Merlin version). Granted, aside from the wings and (initally) tail unit, which were standard P-51 components, most everything else was new and built to British engineering specs. In the end, aside from both Merlin and Griffon powered mock ups (the Griffon version weighed IIRC about the same as a normal Merlin P-51 clean for reference), none ever flew. It should be noted that the fighter version seemingly was intended to be armed with at least a 20mm cannon firing though the prop spinner and probably multiple other wing mounted .50 MGs or 20mm cannons.
And in the end, the Mustang tail was to be discarded for a modified Hawker Tempest tail.
BTW, all the info about the FTB did come from a Key Aero article. Though I was able for some reason to view it on another computer, it's paywalled when I try and look it up on my laptop.
EDIT: Found non-paywalled article:
The involvement of Rolls-Royce’s Hucknall plant in fitting the North American P-51 Mustang with its Merlin engine...
www.key.aero