Green’s Dictionary of Slang

weeny adj.

also weenie
[infant pron.]

tiny.

[US]Ade Forty Modern Fables 111: I like your Style, but I’m a weeny bit Afraid of you.
[UK]T.W.H. Crosland ‘The Diners’ in Coll. Poems 127: (Not just the weeniest bit? / The waiting here’s absurd: / When will they bring the bird?).
[Ire]Joyce Ulysses 225: – ...At last she spotted a weeny weeshy one miles away. And what star is that Poldy? says she. By God, she had Bloom cornered.
[UK](con. 1914) B. Marshall George Brown’s Schooldays 208: We’d both known each other ever since we were weeny weeny little kids.
[US]H. Rawson Dict. of Invective (1991) 412: weeny, meaning a child (from 1844), and ultimately from weeny, meaning something small (1790).
[UK]K. Lette Mad Cows 80: A weenie little ankle-biter like you gets up to eight hundred pounds plus residuals for a TV commercial.