Let me start by quoting the obvious (from Sun Simiao’s Bei Ji Qian Jin Yao Fang, vol. 5 on Pediatrics:

故今斯方，先婦人、小兒，而後丈夫、耆老者，則是崇本之義也。

“Now the present collection of treatments is arranged by placing the treatments for women and children first, and those for husbands and the elderly afterwards. The significance of [this structure] is that it venerates the root.”