c.1200, "save, rescue, set free, liberate," from Old French delivrer "to set free; remove; save, preserve; hand over (goods)," also used of childbirth, from Late Latin deliberare, from de- "away" (see de-) + Latin liberare "to free" (see liberal (adj.)).
Childbirth sense in English, "to bring (a woman) to childbirth," is from c.1300. Sense of "hand over, give, give up, yield" is c.1300. in English, which brings it in opposition to its root. Meaning "project, throw" is 1590s. Related: Delivered; delivering.