equivalent to a broadside of a cruiser.

All of the British 6 inch shell(according to Jane's) weighed the same. The ME would not vary with HC or AP as long as the projectile weight was the same.

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Janes here is almost correct. Comparing the actual datas (for this question it has to be Campbells Naval weapons of ww2) shows only slight differences in weight for UK 6"ers:

6"/50QF MK V (1955):
APC: 129.75lbs
HE: 132 lbs

British 6"/50 (15.2 cm) QF Mark N5

6"/50 BL MK XXIII:
Common: 112lbs
HE: 112 lbs

British 6"/50 (15.2 cm) BL Mark XXIII

6"/50 BL MK XXII:
common: 100lbs
common (from 1942 onwards): 112 lbs

British 6"/50 (15.2 cm) BL Mark XXII

It seems that ww2 era 6" ammo was serialized at around 112 lbs.

Its interesting to compare these figures with the 75mm carried in the B25 which presumably only fired a shell of around 13pds.

Apart from anything to do with rockets, the expression was applied to the Tsetse Mosquito that was equipped with the 57mm auto loading gun as well as the 8 rockets.

Specification of the Molins 6 pounder Anti-tank Gun.

Bore 2.25in (57mm)
Action Recoil
Cyclic Rate 60 rounds per minute
Muzzle Velocity 2,600ft/sec (792m/sec)
Ammo feed Molins automatic
Magazine 22 rounds (some sources say 25)
Length 12ft 5in (3.8m)
Height 38in (965mm)
Weight 1,800lbs (816kg)

Actually, the muzzle velocity of the gun/ammo combination used in the Molins was 890 m/s (2,920 fps). I spent some time tracking down the variations, not helped by the fact that the 6 pdr was made in two different barrel lengths. You can see the results here: Untitled Document