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Slobberer losing a pound with difficulty could be teetotal (5)

Slobberer - lb + er

Obesity run wild leading to self-restraint (8)

Not called to the bar despite being likened to a Judge (5)

Sorority besotted, or this unlikely state? (8)

Composite anag SORORITY+BE / OR SOBRIETY
Sotted is anagrind
In the US, the collegiate "Greek System" (sororities and fraternities) is known for heavy alcohol consumption.

Love spread from cows getting into pigs’ quarters (this is serious!) (8)

love: O
spread (noun) from cows: BRIE
pigs’ quarters: STY
this is serious: SOBRIETY

Cry over half an ale not being full (5)

SOB + (be)ER, a down clue. I'm not sure if the measure of 'half an ale' (285ml) is common outside Au.

Since overdressed beetroot encountered resistance, altogether left off the sauce. (5)

Dryness of cheese on plate? Cover with sauce (8)

So Brie t y

Got him on milk, not alcohol (5)

To paraphrase the great Dr Feelgood

Exchange robes for hair shirt (5)

Hair shirt - def.