In a March 1931 publication of "Sylvan Archer" (a magazine of the period) C. N. Hickman writes that (this is paraphrased folks) the tension of a bow string at brace height is at it's highest tension. then as you draw, the string tension decreases as you approach HALF draw the increases again until full draw is reached. AND, the tension in the string APPROACHES the tension of the string at brace height but doesn't quite reach it.
Now, in the article, he (Hickman) refers to mathematical results that predict this. And then goes on to show testing that confirms the math. In a quick review, I don't see that he addresses the WHY , just the results. For those of you that have an aversion to mathematics and physics this article and most all Hickman's writing are NOT for you. There are formulas and many graphs showing these results.
As a matter of interest, he also talks about the effect of brace height on the weight of the full draw. Basically, A bow's brace height (WITHIN REASON) does not affect the full draw weight of the bow significantly, if at all; but can greatly affect the stress in the limbs. This all was written in a period of time where all wood bows were the norm and linen strings were used. So things MAY have changed but again, maybe not.
A large set of articles written for archery magazines in the 1930s and 1940 are compiled in a book called "Archery _ The Technical Side" and has articles by Hickman, Klopsteg, Nagler and others. For those of you with a math and physics interest, MUCH can be learned from these writers.
There are many examples of things that would APPEAR to make sense that don't stand up to scientific study; I believe this is one of those.
Arne