I think someone found a piece like this a while back. I believe they said it was a colonial picture hanger. This piece gets screwed or nailed to the wall and the picture then hung from this.... Or was it the other way around?
Either way, whatever it is. The hole in the center was the main hole for doing whatever it was that this does/did. The second hole was an after thought.
The second hole was added afterward to keep it from spinning. If it had been original, I think they would have put one hole on either end, as opposed to one in the center and one on the edge.
Good luck figuring out exactly what the piece is! Keep us posted!