Phil ,if you mean the cam on the inside of the flywheel (the part that opens the points) the “counterweight” as you describe it is actually the engine govenor system , the idea being that centrifugal force operates and opens the points too wide for a spark.
Allen Scythes were the only machines that I have seen that use this method , the 25c fitted later also deployed this method.
They will sound rough running without any load , put them into some serious work and they will even themselves out.
Andy.