Forces, or Momentum, the result is the same
Jiff,
regardless of whether you analyse it from the momentum perspective (as Nick Lappos has done correctly) or from the consideration of forces, the net reaction averaged over an entire cycle will be 0.
There are two forces that you need to look at:
1) The reaction force on the base plate of the machine generated by the acceleration and decceleration of the weights. As you have correctly analysed, this will provide a net average force in one direction over an entire cycle.
2) The centripetal force required to keep the weights moving in a circle (this is the force of constraint provided by the arms the weights are mounted on). As the weights are travelling at a faster speed on one side of the cycle, and slower on the other side of the cycle, the average centripetal force exerted by the baseplate on the rotating masses is not zero.
These two forces will end up cancelling each other out over an entire cycle.
Daniel