1570s, "inferior in rank" (1540s as a noun, "junior pupil, freshman"), senses now obsolete, from French puisné (Modern French puîné), from Old French puisne "born later, younger, youngest" (12c., contrasted with aisné "first-born").
This is from puis nez, from puis "afterward" (from Vulgar Latin *postius, from Latin postea "after this, hereafter," from post "after," see post-, + ea "there") + Old French né "born," from Latin natus, past participle of nasci "be born" (Old Latin gnasci; from PIE root *gene- "give birth, beget"). Compare puisne.
The sense of "small, weak, insignificant, imperfectly developed in size or strength" is recorded from 1590s. Related: Puniness.