Green’s Dictionary of Slang

1. (usu. Aus./N.Z.) cowardly, weak, sentimental.

1901		Bulletin (Sydney) 2 Nov. Red Page: Big, sooky-looking fellow he was, with ears like little turn-over tarts.
1953		D. Cusack Southern Steel 238: Get along with you: you’re getting real sookey [AND].
1959		A. Sillitoe ‘The Disgrace of Jim Scarfedale’ Loneliness of the Long-Distance Runner (1960) 133: Sucky Jim would jump out of his hiding-place near pieces of waste ground and frighten the life out of them.
2005		P. Temple Broken Shore (2007) [ebook] Poodles are sooky little things.

2. (Scot.) servile.

2012

(con. 1980s) I. Welsh Skagboys 501: We baith look like jakeys but the staff cats ur bein ultra sooky cause ay it being her.