at take off the B29 Enola Gay was 7 tons over weight
Little Boy weighed in at 9,700 lbs and Fat Man 10,300 so I venture the B-29 was not overweight structurally, details for the Enola Gay give the max permissible gross as 140,000, same as the regular B-29. Due to failures of the US system, British Type G single-point attachments and Type F releases as used on the Lancaster B.I Specia
l to carry the 12,000-pound (5,400 kg) Tallboy bomb were used for the atomic bomb.
Ditching on take off was a regular event for the Tinian B-29's, engine over heating being a major issue, maintenance learnt that engine baffles had to be in good order to avoid overheating. At the start they were only getting 100 hours out of an engine. On Tinian take off began with gills full open with the engineer keeping an eye on CHT's and progressively closing the gills as the aircraft accelerated, important factor as open gills caused so much drag and impeded acceleration.
For specific operations, military aircraft can be authorised to operate at greater mass within certain carefully defined criteria
WWII limits were rather loose. Pilot flying the C-46 across the Hump says many flights were above even the emergency overload weight of 50,000lb, normal being 48,000lb.
For ferry flights the authorities will grant an overweight operation permit, if flying in Alaska the FAA grant a 15% increase in gross weight under FAR §91.323 for aircraft under 12,500lb.