Wow, I'm off for a couple of days and tons of new posts. Welcome to my misery...Glad someone else is obsessed with figuring out what these things are. Here are a few comments:
Distance between the balls is approx an inch....BARELY a finger width.
Connecting rod is solidly attached and from what i can tell and not threaded and screwed on. With that said, they have been a field for a very long time and rust would have prevented any threaded or sliding action to work properly now.
No way it could be a barbell, although that's what it looks like at first glance. Distance between isn't wide enough.
I say 20#....i havent weighed them, just a guess...I can weigh them if that would help any.
Barshot....As much as I'd like these things to be exactly that, I do find it difficult to believe that to be possible. Location of the find....middle of farm country AND the bar shot pictures I have seen are much farther apart. I suppose it would be possible to get transported here, but that would be like finding a shark tooth out in a field - know what i mean?
Weight of some sort? By far the most logical idea to me. The distance between them would make it possible to attach via a rope, or the rope could have been rolled up around the shaft.
No signs of wear of any sort on the balls makes this a logical conclusion also - but what for?
One final thought, just thought of this as typing this. It has been noted that the balls have a cut out area larger than the shaft...could there have been a larger "sleave" over the top of the connecting rod? This would have changed the "gear ratio" of one wind of a rope. Maybe a wooden sleave that has decayed over time? Just a wild thought, not sure why a sleave over the rod would be necessary, but could possibly explain the larger diameter in the balls.