It's  3 3/4" long  -  1 5/8" dia. - & 2"dia. and weighs  2 lbs 4 oz.

Not sure of it's original purpose, but looks like you could balance a lawn mower blade with it.
Probably a center for a lathe?

Really big dowel centering pegs? For transferring hole centers?

center for a lathe

Hard to tell from the third photo down but it looks like unpointed end has a hole in it.  If so, it could be a plumb bob — home made?  The pointed end would need to screw or otherwise come off in order to insert a stash of string.  And at 2 lbs. 4 ozs., it'd hold still in a pretty good gale, I reckon.

In the 2nd picture the shaft looks tapered, is that correct? I'd toss my vote in with the lathe center group.

Chilly