Piece of cake. Build a simulator, that is, an exact replica of the size or wire or string, the length, and fix one end of the string to an anchor, and the other end over a pulley with a weight on it. Now take a spring scale such as those used by fishermen and hook your stretched string in the middle. Have a piece of paper behind the line and mark the paper along the straight line. Now hook onto the middle of the string and apply pressure. Measure the distance in inches or centimeters, and write down the pull in pounds or grams at different distances. Now change the weight on the string and repeat the experiment. With this information in hand you can do a simple proportional formula extrapolation for the unknown in your actual case.
Let us know what happens since this seems to be a very interesting thread.
Wayne