Green’s Dictionary of Slang

blown up adj.

[SE blow, to explode + ? image of a bloated drunkard]

(US) drunk or overindulging in drugs.

[US]Eble Campus Sl. Apr. 1: blown up – drunk.
[US]Eble Sl. and Sociability 45: Overindulgers in alcohol or drugs are pictured as the objects of various kinds of destructive processes: explosion (blasted, blown out, blown up, bombed).