c. 1300, despit (n.) "contemptuous challenge, defiance; act designed to insult or humiliate someone;" mid-14c., "scorn, contempt," from Old French despit (12c., Modern French dépit), from Latin despectus "a looking down on, scorn, contempt," from past participle of despicere "look down on, scorn," from de "down" (see de-) + spicere/specere "to look at" (from PIE root *spek- "to observe").
The prepositional sense "notwithstanding" (early 15c.) is short for in despite of "in defiance or contempt of" (c. 1300), a loan-translation of Anglo-French en despit de "in contempt of." It almost became despight during the 16c. spelling reform.