able-bodied (adj.)

"having sufficient power or means," early 14c., from Old French (h)able "capable; fitting, suitable; agile, nimble" (14c.), from Latin habilem, habilis "easily handled, apt," verbal adjective from habere "to hold" (from PIE root *ghabh- "to give or receive").

"Easy to be held," hence "fit for a purpose." The silent h- was dropped in English and resisted academic attempts to restore it 16c.-17c. (see H), but some derivatives (such as habiliment, habilitate) acquired it via French. Able seaman, one able to do any sort of work required on a ship, may be the origin of this:

Able-whackets - A popular sea-game with cards, in which the loser is beaten over the palms of the hands with a handkerchief tightly twisted like a rope. Very popular with horny-fisted sailors. [Smyth, "Sailor's Word-Book," 1867]

Old English bodig "trunk of a man or beast, physical structure of a human or animal; material frame, material existence of a human; main or principal part of anything," related to Old High German botah, but otherwise of unknown origin. Not elsewhere in Germanic, and the word has died out in German (replaced by Leib, originally "life," and Körper, from Latin), "but in English body remains as a great and important word" [OED].

Extension to "a person, a human being" is from c. 1300. Meaning "main part" of anything was in late Old English, hence its use in reference to vehicles (1520s). From 1580s as "part of the dress which covers the body." From 1590s as "main part of a group, any number of individuals spoken of collectively." From 1660s as "main portion of a document." Contrasted with soul at least since mid-13c. Meaning "corpse" ("dead body") is from c. 1200. Transferred to matter generally in Middle English (as in heavenly body, late 14c.).

Body politic "the nation, the state, whole body of people living under an organized government" first recorded late 15c., with French word order. Body image was coined 1934. Body count "number of enemy killed in battle or otherwise" is from 1968, from the Vietnam War. Body language is attested from 1967, perhaps from French langage corporel (1966). Body-snatcher "one who secretly disinters the bodies of the recently dead for dissection" is from 1834. Phrase over my dead body attested by 1833.