Green’s Dictionary of Slang

(Irish/Scot.) a small or large number.

1913		A. Irvine My Lady of the Chimney Corner 77: ‘Haave ye aany marbles, dear?’ she asked me. ‘Aye, a wheen.’.
1925		L. Doyle Dear Ducks 93: For a wheen of weeks nobody seen him at all.
1951		S.H. Bell December Bride 184: We canna put the craturs out on the road for a wheen av bags o’ corn and praties!
1965		B. Behan Confessions 223: Numerous canty bodies make a wheen of ha’pence on the export trade.
1995		I. Rankin Let It Bleed 92: Those are two questions; I’ve got a wheen more.