I have one suggestion that probably isn't 100% accurate, but may get the general results you're looking for. If you put a scale under whatever body part you're "resting" (keeping out of the exercise due to strength constraints), the scale will display the amount of mass that the "ground" (scale) is supporting, rather than your working muscles. For example, if you rest your feet on a scale instead of the floor while you're doing your dips, it will display a certain value. If you subtract this value from your bodyweight, you get the amount of weight that you are supporting with your triceps. This method also has the advantage of being a sort of "point of reference" to your form. If you have good form, the needle on the scale (or digital display) won't fluctuate much as you do the exercise. If, however, at a certain point in the movement you start to lean forward more, putting more weight on your feet (and the scale/ground), you will see a sudden increase in the amount of mass being supported by the scale that may not be recognizable if you were doing dips without it there.
Similarly, while doing pushups, you could "push up" against the scale to see how much of your bodyweight you are pushing up with your arms, and how much is supported by your feet. My guess is with a little ingenuity one could find a creative place to put the scale in just about every exercise.
Like I said, it probably isn't 100% accurate, but it may help get some of the results you are looking for. It wouldn't be very useful in calculating the (often cruel) leverage dis/advantages we put ourselves under while using bodyweight exercises, but as a basic measuring tool it might be rather useful. I think I might have to try it out with my workout tonight
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N.B. In Pavel's "The Naked Warrior" he implemented another interesting, similar use of a scale. He wanted to see exactly how much benefit came with engaging multiple muscle groups to utilize their assistance in bodyweight exercises (notably by clenching his hands into a fist, engaging his abdomen and engaging his glutes). He stood on a scale and proceeded to get in an "iron cross" position on a pair of rings (often seen in men's gymnastics, where the body is held isometrically between two rings with the arms outstretched so the body is in a "T" configuration), but put himself at such a leverage disadvantage he knew he would never be able to lift his full bodyweight off of the scale. He lifted as much of his bodyweight as he could, using only the necessary muscles, and then he engaged the seemingly less necessary grip strength, glutes, and abdomen. He was amazed to find that because of the effect he calls "completing the chain", he was able to lift about 40 more pounds of bodyweight off of the scale when he engaged these three muscle groups.
