Ok, just to fix your terminology here - there is no such thing as "Class 3". The term is an industry specific definition of taxpayer for those that are importers, manufacturers or dealers.
Anyways - since supressors are regulated as Title II or NFA - say Title II or NFA.
Since I wasn't around in 1934, I checked the wikipedia and apparently they wanted something to stop the gangland violence that was happening across the country and passed the law wanting the very expensive tax on SBR'SBS guns, on machineguns and anything to muffle the sound of a firearm.
I suspect it is because they percieved a silencer to be one of those things that fall in the "If you own one of these, you must be up to no good" category. Like fast cars, faster women, machineguns and a few cases of Jack Daniels.