Here are some similar idioms that convey a similar meaning:
* Bully the weak: This idiom directly refers to the act of using power to intimidate or harm those who are less powerful.
* Pick on someone smaller than you: This idiom emphasizes the unfairness of targeting someone who is less able to defend themselves.
* Kick someone when they're down: This idiom refers to taking advantage of someone's weakness or vulnerability.
* Pick a fight with someone who can't fight back: This idiom emphasizes the cowardice of attacking someone who is unable to defend themselves.
While "picking on the weaker man" isn't a formal idiom, it clearly conveys the concept of targeting someone who is vulnerable, making it a powerful and widely understood phrase.