Could it be half a door knob. I had brass door knobs with a metal bar that went through the hole. One knob with attached bar was poked through hole and screwed into the knob on the other side.
Heck, all this talk about screws, knobs and holes, I'm feeling quite light headed.
Sit down and take a glass of water Granny.Dont think it would be part of a door knob as its got no fixing points.
The hand bit is screwed tight and none of it moves. Possibly just a boring paper weight . Not even sure what it is the hand is gripping--just looks like a straight bar. Not broken off. Base and hand look different materials cast iron and brass. Pattern on base is oak leaves and acorns