Assuming no friction and given a fast tug of the rope I still don't think the near equal weight would hold still or sink while the other near equal weight flew

Assuming no friction and given a fast tug of the rope I still don't think the near equal weight would hold still or sink while the other near equal weight flew up quickly. With the large weight difference, I think the required speed of pulling the rope to make them both rise just becomes impractically fast. Imagine the system in space - all the weights would move up, so they all have an upward force applied to them from the rope tugging. It's just a matter of pulling so fast that that upward force overcomes gravity.