Here is a comparison of the "HB" 36-1 with its 3" tapered barrel siblings the 36 and 37 no dash .
I wouldnt call the older 3" tapered barrel "Heavy" as it appears to be a longer version of the 1 7/8" snub barrel lengthened at the rear instead of the front.
The top gun is the 3" Mod 37 ,
Have not heard of a 37 with a 3" HB and imagine it kinda defeats the purpose of the Airweight frame.
Notice the differences in the amount of checkering ,
seems to have got larger then shrunk as production went into the mid 70's .