The counterweights are two large chunks of metal on the upper (movable) part of the Director. The weights are adjusted fore and aft when the MK14 or another Gunsight is initially installed. They balance the upper portion of the director, so the operator does not have to push the handles down to counter the full weight of the gunsight. The handles are like those on a bicycle, except that you use them to train left and right for full rotation, and to elevate/depress for a range of about 110 degrees.
Yes, I will be there during LST Week for my ship's annual reunion; and could train you as a MK 51 Director Operator if we have the time. The only thing difficult about it would be seeing through the optics, and the fact that we have no electrical power to operate the gyros or reticle. Climbing the ladders into the tubs might also be a bit difficult, but is certainly easier and safer now that the guys have refurbished them.