Green’s Dictionary of Slang

weenchy adj.

[weeny adj.]

(US) tiny, very little.

[US]Wolfert Und. 415: Just a weenchy [...] little dash of perfume [W&F].
[US]Wentworth & Flexner DAS 571/1: [...] Dial. use since c1900.
S. Bowman ‘Salinger’s Problem with Westerners’ posting 23 Oct. at [Internet] Yocum & Patrick sound a good deal more serious about books than I ever was. But to consign the three of us, & our like, implicitly, to the ranks of the knuckle-trailers is a teenshy, TEENSHY, weenchy bit – dare I say it ? – arrogant.