What is the origin of "breaking one's balls"?

Solution 1:

According to The New Patridge Dictionary of Slang and Unconventional English to bust someone's balls "to tease someone relentlessly, provoking their anger" is an AmE expression from 1955 •

The following source states that the expressions break/bust somebody's balls derive from the practice of cattle castration. It is not clear if there is a connection with the similar Italian expression but it appears that it was made popular by the 1990's movies Goodfellas. See also Ngram:

  • Whether it’s busting or breaking, balls or stones, this expression has long been used by young men (and not a few women) to express a wide range of emotions brought about by the words or actions of another.

  • Although the phrase usually accompanies laughter, it arose out of a truly painful, yet common practice among beef cattle operators where they bust the bull’s balls as a method of castration.

Popular Usage

  • For those not familiar with the phrase, there are a couple of different common meanings to “bust your balls.” Both of the following examples come from the 1990’s movie, Goodfellas.

Teasing:

The first, and far more common, is when someone is being teased or kidded:

  • Tommy: Just don’t go busting my balls, Billy, okay?

  • Billy: Hey, Tommy, if I was gonna break your balls, I’d tell you to go home and get your shine box.

Abusive:

The second, and by far the more nefarious, is when someone is overworking, overwhelming or trying to ruin another:

  • Jimmy: Give me the fuckin money, You hear me? You hear me, I gotta come here and you bust my balls? Give me the fuckin money.

From: (www.todayifoundout.com)