For a Bear Hug?

In wrestling, a bear hug, also known as a bodylock, is a grappling clinch hold and stand-up grappling position where the arms are wrapped around the opponent, either around the opponent's chest, midsection, or thighs, sometimes with one or both of the opponent's arms pinned to the opponent's body.

What is the meaning of a bear hug?

: a strong and rough hug : an act of showing affection by putting your arms around someone and squeezing very tightly. Comments on bear-hug.

Why is bear hug a common saying?

An affectionate, sometimes overwhelming embrace. In wrestling it is also known as a body lock; in business it is an aggressive offer for a takeover. But the cliché refers simply to the embrace, as in “Jane met him with a handshake, but he responded by giving her a bear hug.”