Green’s Dictionary of Slang

heady adj.2

[the contents of one’s head]

1. (mainly Aus./N.Z.) ingenious, shrewd.

[NZ] McGill Reed Dict. of N.Z. Sl.

2. (US) arrogant, opinionated.

[US]Sporting News 19 Dec. in Fleming Unforgettable Season (1981) 9: Bridwell [...] will look like an amateur in the absence of the heady Dahlen.
[US]M.G. Hayden ‘Terms Of Disparagement’ in DN IV:iii 214: heady, [...] opinionated. ‘That fellow is heady since his father was elected president.’.