The letters A,B,C, D, and DD refer to, OH, Gun Barrels, right
!!
They refer to the overall size of the barrel at the breech, waist, and muzzle. They don't necessarily correlate to the actual weight of the barrel. A "B" weight 40 caliber barrel will weigh more than a "C weight 54, as the thickness of the barrel wall is more.
IIRC, a B weight barrel is just shy of 1" at the breech, a C weight is about 1 1/16", etc.
-Eric