1520s, "sideways, asquint," of obscure origin. OED has separate listings for askance and obsolete Middle English askance(s) and no indication of a connection, but Barnhart and others derive the newer word from the older one. The Middle English word, recorded early 14c. as ase quances and found later in Chaucer, meant "in such a way that; even as; as if;" and as an adverb "insincerely, deceptively." It has been analyzed as a compound of as and Old French quanses (pronounced "kanses") "how if," from Latin quam "how" + si "if."
The E[nglish] as is, accordingly, redundant, and merely added by way of partial explanation. The M.E. askances means "as if" in other passages, but here means, "as if it were," i.e. "possibly," "perhaps"; as said above. Sometimes the final s is dropped .... [Walter W. Skeat, glossary to Chaucer's "Man of Law's Tale," 1894]Also see discussion in Leo Spitzer, "Anglo-French Etymologies," Philological Quarterly 24.23 (1945), and see OED entry for askance (adv.) for discussion of the mysterious ask- word cluster in English. Other guesses about the origin of askance include Old French a escone, from past participle of a word for "hidden;" Italian a scancio "obliquely, slantingly;" or that it is a cognate of askew.