Rigidly conventional, as in manners, opinions, and tastes: "She sees this headlong, headstrong, plunge into worldliness as a protracted process of shucking the shame of her uptight upbringing"(James Wolcott).
mod. anxious. : Dave always seems uptight about something.
Dictionary of American Slang and Colloquial Expressions by Richard A. Spears.Fourth Edition. Copyright 2007. Published by McGraw Hill.
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Word Origin & History
uptight
Slang sense of "tense" is from 1934; that of "straight-laced" first recorded 1969. It was used in a sense of "excellent" in jazz slang c.1962.
[uhp-tahyt] 
