Old English bodig "trunk, chest" (of a man or animal); related to Old High German botah, of unknown origin. Not elsewhere in Germanic, and the word has died out in German (replaced by leib, originally "life," and körper, from Latin). In English, extension to "person" is from late 13c. Meaning "main part" of anything was in late Old English, hence its use in reference to vehicles (1520s).
Contrasted with soul since at least mid-13c. Meaning "corpse" (short for dead body) is from late 13c. Transferred to matter generally in Middle English (e.g. heavenly body, late 14c.). Body politic "the nation, the state" first recorded 1520s, legalese, with French word order. Body image was coined 1935. Body language is attested from 1967, perhaps from French langage corporel (1966). Phrase over my dead body attested by 1833.