YOU try being the only sober at a party – all the time – and see what the other party folks think of you.

I say I'm abstemious because I do enjoy a margarita or two every other month, roughly.
They say I'm square because I only enjoy a margarita or two every other month. And don't smoke anything fun.

My first thought is that it would relate to abstaining, which would be not doing anything at all, rather than moderation.

However, I checked dictionary.com and they show the following options to be either moderate or abstaining completely.

ab⋅ste⋅mi⋅ous  /æbˈstimiəs/ Show Spelled Pronunciation [ab-stee-mee-uhs] Show IPA
–adjective 1. sparing or moderate in eating and drinking; temperate in diet.
2. characterized by abstinence: an abstemious life.
3. sparing: an abstemious diet.


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Origin:
1615–25; < L abstēmius, equiv. to abs- abs- + tēm- (base of tēmētum intoxicating drink) + -ius -ious

Related forms:

ab⋅ste⋅mi⋅ous⋅ly, adverb
ab⋅ste⋅mi⋅ous⋅ness, noun


Synonyms:
ascetic, abstinent, temperate, nonindulgent.

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.