Much is made of the problems associated with the imbalance of the up and over shutter during its "wayward" travel.
The heavy shutter has first to be lifted to open.
Then restrained from destroying itself at the back of the dome after its CofG passes over the zenith.
However, the shutter could be balanced by two equal counterweights on supporting ropes, cables or chains.
Given the nature of a dome's rotation this might cause the counterweights to drag along the ground.
Obviously this can't be allowed to happen.
The answer is to stop the weights from reaching the ground by means of a stop on the cable, chain or rope.
The opposing counterweight then finds itself in full control of the shutter during opening or closure.
While the automatically "stopped" weight is relieved of all duty.
An automatic counterbalance system without the need for human intervention.
The stop could be as simple as a screw eye and a knot in the weight supporting rope.
Or as complex as you like in a driven open/close system.
The "stop" would obviously cause the supporting cable [chain or rope] to go loose and bunch up above the stop.
Fortunately, tangles can be safely avoided with a pulley, a Huygenian endless loop and smaller counterweight to maintain tension.
The entire shutter can be thought of as a sector of a widely spaced pair of pulleys.
One on each side of the shutter.
A pair is needed because you don't want a rope in the middle of the open observing slit.
Though the "rear" weight [opposite the slit] could use a single rope for simplicity.
The following image shows the basic idea.
I claim no originality for this idea which just popped into my head as I worked on my own, bi-parting shutters.