Consider if you will the peculiar origins of askance.
These days, the word is mainly used in phrases such as “to look askance”, meaning to look at (figuratively or literally) with distrust, suspicion etc.
The earliest examples of the use of this word as an adjective or adverb appear to relate to looking obliquely or sidelong. The earliest cite is from 1530.
Of the etymology, OED says:
Perhaps a specific sense development of askances adv. (compare β. forms at askances conj. and adv.), perhaps arising by association with askoy adv. or asquint adv., both of which are attested earlier in similar senses and constructions.
“askances conj and adv.” is an obsolete form meaning “as if”. The earliest cite is from the c1350, and going by the OED cite list it fell out of use in the 16th century. Example:
a1586 Sir P. Sidney Arcadia (1590) ii. xvi. sig. Z6v Keeping a countenance ascanses she vnderstood him not.
There are also a few cites, from 1450 to 1500, for a more specific meaning of “askances adv.”: With affectation, artificially, insincerely; deceptively.
It’s easy to believe that the succession of meaning went: “askances adv. meaning as if” to “askances adv. meaning insincerely” to “looking askance meaning looking sidelong”.
Askances, in turn, appears to come from “as quanses”. As is a Germanic-derived English word, and quanses was a borrowing from the French, meaning “as if, feigning, as if to say”. Quanses derives from the Latin quam si, meaning “as if”. Quasi, funnily enough, has the same origin.