Capt Quentin McHale, I think the answer to your question lies in visualizing the cable run to the back end of the aircraft. The cable is likely supported at regular intervals along its length, and forms catenary arcs in between the points of support.
(In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.) The droop in each catenary segment is dependent upon cable tension.
As you increase tension in the cables, they approach a straight line segmenst between the points of support and act like tension springs.
Another factor to consider is that with large aircraft, there is a significant difference in the rates of thermal expansion between the steel control cables and the aluminum structure. Larger aircraft have tension compensating devices incorporated at the points of cable termination to allow for these differences. These tension compensating devices are normally springs.