Another really good question. Where does the phrase, "hit it off" originate from? I don't know :) Let's guess, could it be from, maybe like a game of baseball, where the ball hits off the bat?? And they score - whatever people score in baseball?? Meaning success? Throwing a ball at a coconut at the funfair?? Knocking/hitting it off the stand, to win a prize?? = happy success?? I'm going to google it, and see what I get

To get along well with someone almost instantly. "I hit it off with a girl named Sarah. Now we are best friends."

"Hit it off" is an idiom or verb phrase that means to be comfortable in each other's company. You enjoy being together, and get along well with each other. Some people "hit it off" when they first meet each other.

the idiom and the context seem (to me) to be coherent with: to hit off {sadness, melancholy} with a [newly acquired] friend.

To hit something away. To hit something until you emotions come to normal levels.