Green’s Dictionary of Slang

narrow-assed adj.

also narrowgutted
[SE narrow + ass n. (2)/SE gut]

(US/UK) slim, skinny; thus narrow-minded.

[US]H.N. Cary Sl. of Venery.
[UK]J. Franklyn Cockney 275: A thin man whose nickname is actually ‘Narrowgut’ will be known simply as ‘Narrow’.
[US]H. Rhodes Chosen Few (1966) 136: His narrow-ass deputy and a coupla white MPs are on their way over.
[Aus]D. Ireland Burn 109: Not if my glorious narrow-gutted, narrow-minded Australian workmates had any say in it.