Abstract: A deep well pump jack having a walking beam pivotally mounted on a Samson post with sucker rods depending from one end of the walking beam and a counterbalancing weight carried by the other end of the walking beam, and a prime mover is provided to rock the walking beam up and down in operation through pumping cycles. During pumping cycles, the counterbalancing weight is moved or driven in movement relative to the walking beam such that the center of gravity of the counterbalancing weight follows a vertical pattern of movement throughout each pumping cycle wherein the center of gravity travels in a substantially straight line while traveling upward and in a line of curvature directed outwardly away from the Samson pivot while traveling downward to compensate for the varying loads placed on the prime mover during each pumping cycle.