From Old French (13th century), from Proto-Indo-European '*speḱ-' ("to observe, to look"), from PIE *speḱ- ("to observe, to look").
A desire to hurt, annoy, or offend someone; deliberate malice; ill will.
Shortened from Old French 'despit' (contempt, scorn, disdain), from Latin 'dēspectus' (a looking down upon, contempt), past participle of 'dēspicere' (to look down on, despise), from 'dē-' (down) and 'specere' (to look). 'Spite' is literally a 'looking down' — contempt distilled into active malice. The same Latin root gives us 'despise,' 'despite,' and 'despicable.' The shortening from 'despite' to 'spite' in English
'Spite' is etymologically related to 'respect' and 'spectacle' — all descend from PIE *speḱ- (to look). 'Respect' is looking back at someone (re-spicere), 'spectacle' is something worth looking at, and 'spite' is looking down on someone (de-spicere). Three completely different emotions, all rooted in the act of seeing.