OK, the thing has three hammering surfaces on the striking side and a rounded indentation on the bottom. It's some kind of a tool to round off a protrusion by hammering it down and if either side sticks up you can hammer it down too.
Not made for rounding off a protrusion. Think back to the discussion we had about counterweights and some of their applications. This tool is used in one of those applications.
Alright, another clue. Martin had a guess in the counterweights discussion that has something to do with this tool.
Finally! You are absolutely right. It is a pulley driver for the old windows that had ropes, pulleys and weights in the sash, the pulleys were driven into the mortise with this tool. From martin's post #500 in this thread:
How can anybody be right who uses the technical term "doohickey". The answer is counterweight doohickey? Seriously?