Once both sashes are out of the window frame, pry open the secret doors in each side of the frame. These are the weight pockets. I am sorry to say that to open both pockets you might have to remove both parting beads. Once they are open you can replace your dirty, broken ropes or rusted, painted chains with flat sash chain that lasts forever.
There should be four weights in all - one for the lower and one for the upper sash on each side. New weights are hard to come by - see if your old weight is somewhere inside the pocket. Most hardware stores sell sash chains and they can tell you how to attach them. Many will also be able to tell you where to find used sash weights
When your window was first made, each sash opened smoothly and stayed put. The pulleys were fastened to the frame and well oiled. The chains were attached to the sash at one end and to the weight at the other. They ran smooth and flat over the pulleys. The weights and chains were not tangled up inside the pockets. The chains were long enough to let the sashes travel up and down and short enough to keep tension on the weights even when the window was closed. With only occasional maintenance, this low-tech mechanism will last for another hundred years.