Remove the screws from the stops on each side of the window. Remove the stops.
Pull the sash out of the window.
Pull out the parting bead that holds the top sash in the window. Pull out the top sash.
Cut the weight rope. Tie the rope into a knot to keep it from falling into the wall.
Remove the screws from the weight access panels to expose the weights.
Pull down on the knotted rope to lift the weight. Tie your new rope to the old knotted rope. Allow the weight to drop to pull the new rope through the weight access panels. Cut the old rope to remove it from the weight.
Tie the weight to the new rope. Cut the new rope to length, tie it to the window sash and reassemble.