It looks as if it may only be about 2 mm thick, so I doubt it will create enough imbalance to damage the engine.
The question seems to be, what would cause an imbalance that would require correction by that weight? Two possibilities come to mind.
The first possibility, is the problem associated with failure of the captive cotter. That seems to result eventually in the whole clutch running out of true, after the engine-side key gets mixed up in the thrust bearing and levers things about, creating clearance of the left side clutch half on the engine shaft. The resulting runout of the clutch seems to be the source of the vibration that breaks the engine mounting deck. We haven't proved that, but it seems a plausible explanation on the evidence we've seen so far. What we need is more cases and more experiments with partial cures. Now, perhaps someone noted the vibration that is caused by this issue, and thought a counterweight might alleviate the problem.
The other obvious possibility is that some of the clutches were out of balance. That could happen if the two halves did not mate perfectly where they clamp up against each other. Because there is a self-aligning bearing at the chaincase end of the clutch shaft, and the engine mounting deck is fairly flexible, at least on the twin rail versions, any slight mismatch of the mating faces of the clutch would cause the whole rotating system (two shafts and a large clutch in the middle) to become V-shaped instead of a straight line. A rotating imbalance of the whole clutch would result. That would cause a noticeable vibration. If that were a known problem, there might have been a counterweight available as a service fix for the vibration.
These are just guesses, Deejay. There are still plenty of mysteries to solve regarding that clutch, its shafts and keys, and vibrations in the machine.