Green’s Dictionary of Slang

1. (US) a silly fool; thus as adj., foolish; mawkish, sentimental.

1913		Van Loan ‘Will a Duck Swim?’ in Lucky Seventh (2004) 253: The goo-goo girlie in the grand stand who inspires the hero to knock the ball over the fence.
1933		T.T. Flynn ‘The Deadly Orchid’ in Goodstone Pulps (1970) 104/2: Lay off that goo-goo talk.
1958		(con. 1890s) S.H. Adams Tenderloin 172: That’s more than you can say for some of the goo-goo sons-a-bitches he’s got working on it.
1972		B. Rodgers Queens’ Vernacular 98: goo goo stuff (dated) excessive romanticism; mush.
1989		H. Rawson Dict. of Invective (1991) 5: The use of alliteration and rhyme, as in boob tube, claptrap, crumb bum, flim-flam, gobbledygook, goo-goo, rinky-dink, ticky-tacky, and wishy-washy.
1994		J. Wambaugh Finnegan’s Week 310: She’s obviously ga-ga over the big-city detective. Or is it goo-goo at her age?

2. see goo-goo eyes n.