IIRC S&W has not manufactured any tapered-barrel M10s in the last 15-20 years except for a very limited special distributor run of ~500 units 4-5 years ago with color case frames. Interestingly, they have earmarked several recent engineering dash numbers for tapered-barrel versions, but AFAIK the experts seem to agree that no guns were actually built for public sale.
The 4" heavy barrel has been offered since the early 1960s, and IIRC a 2" heavy barrel was offered from the late 70s until ~1990 when the 2" guns were more or less dropped from standard production. All 3" guns have heavy barrels but they are generally quite uncommon. AFAIK there is no such thing as a 5" or 6" heavy barrel M10.
IIRC a 4" HB M10 weighs ~36oz empty. My 4" tapered barrel with a Tyler T-Grip weighs almost 34oz loaded with six 158gr rounds, so I believe the weight difference is a bit more than 4oz empty.