Green’s Dictionary of Slang

weatherheaded adj.

[SE weather; the image is of the fool’s head turning like that of a weathercock; Hotten prefers SE wether, a ram, thus the person has a ‘sheepish’ look]

foolish, simple.

[UK]Congreve Love for Love II i: Sir, is this the usage for your son? For that old, weather-headed fool, I know how to laugh at him.
[UK]Hotten Sl. Dict. 267: WEATHER-HEADED, as written by Sir Walter Scott [...] but it is more probably wether-headed, as applied to a person having a ‘sheepish’ look.
[UK]Sl. Dict.
[US]E. Dahlberg Olive of Minerva 167: I laugh at your scrubby triumphs [...] and your infantine mischief with weather-headed slovens.