"piece of a barrel," 1750, back-formation from staves (1398), plural of staff (cf. leaves/leaf), possibly from O.E., but not recorded there. The verb (to stave in, past tense stove) is c.1595, originally nautical, on notion of bashing in the staves of a cask and letting out the contents; stave off (c.1624) is lit. "keep off with a staff," as of dogs.
Thank you, Shu! I love to laugh, and you made me laugh so hard with your hilarious eye-rolling "sheesh" comment. I like the way you posted this question because this way I got to read a fascinating discussion through tears of laughter. Of course, I didn't have to look anything up either...
Even though it is perfectly simple to answer your own question - there'd be no point in a board like this if you could not discuss it, would there? Makes the whole topic more enjoyable.