mid-14c., "substance added to dough to produce fermentation," from Old French levain "leaven, sourdough" (12c.), from Latin levamen, which in literary use meant "alleviation, mitigation," but in Vulgar Latin it had a literal sense of "means of lifting, something that raises." It is from levare "to raise" (from PIE root *legwh- "not heavy, having little weight"). Figurative use is from late 14c., "[c]hiefly with allusion to certain passages of the gospels" [OED]. Related: Leavenous.
"excite fermentation in," c. 1400, leueyn, from leaven (n.). Figurative sense "work upon by invisible or powerful influence" is from 1540s. Related: Leavened; leavening.