Fundamental to understanding their function, a Lycoming "counterweight" is not really a counterweight. They're mounted 90 degrees to the crankthrow, so they only thing they counterweight is themselves.
Calling them counterweights is mere poor terminology in common use, like "radiator" for heat exchanger or "shock absorber" for damper. They are tuned centrifugal pendulums, or to be more precise, the particular type used in a Lyc is a bifilar pendulum absorber. Their purpose is to eliminate torsional vibration at a particular tuned frequency.
Having considerable mass, a pendulum absorber can be arranged on a crank to serve a dual role of pendulum absorber and counterweight to piston/connecting rod mass. However, that's just the designer being thrifty with weight. If he only needed a counterweight, a mass solidly fixed to the crank would be fine.
Ryan, there's a decent discussion of pendulum absorbers in Schwaner's "Sky Ranch Engineering Manual", although the pendulum equations on pg 425 of my edition contain errors. Regardless, the book is a worthwhile addition to your personal library, along with his magneto manual. A more technical discussion can be found in any of the classic books on vibration.