Green’s Dictionary of Slang

(W.I.) affected, putting on airs.

1983		T. White Catch a Fire 224: ‘Small Axe,’ another ‘cockaty’ (boastful) Perry salvo that warned the Big T’ree Jamaican studios that Upsetter Records new band [etc.].
1995		Francis-Jackson Official Dancehall Dict. 11: Cockaty to affect airs: u. de gal a gwaan too cockaty/she is much too affected.