Green’s Dictionary of Slang

a hard look; a serious, studious look.

1913		T.A. Dorgan in Zwilling TAD Lex. (1993) 33: You go to the cooler for 30 days and give that the double o awhile.
1917		R. Lardner ‘Three Kings and a Pair’ in Gullible’s Travels 48: So then I and Bishop knocked the street-car service and President Wilson and give each other the double O.
1921		C.B. Booth ‘Mr Clacksworthy Within the Law’ Detective Story 13 Aug. 🌐 You ain’t tryin’ to tell me that a wise guinea like old Denton is handin’ out any fifty-thousand-dollar checks until he’s give the deal the double-o?
1921		N. Putnam West Broadway 51: I gave it [i.e. a roadmap] the double O and, as the poet says, a world of romance commenced to spread before me.
1935		J.S. Parry ‘Night Scene’ in Spicy Detective Stories May 🌐 She was giving Donovan a furtive double-o.
1949		I. Shulman Cry Tough! 196: Andy didn’t like having strangers giving him the double-o while he ate.
1955		B. Schulberg On the Waterfront (1964) 118: Every one [...] who offered himself to Big Mac’s cynical double-o.
1962		Ragen & Finston World’s Toughest Prison 797: double o – An observation or spying.
1980		A. Pearl Dict. Popular Sl.