What is the difference between "take it easy on" and "take it easy with"? For example, which of the following is correct:
Take it easy on me.
Take it easy with me.
I think that you are maybe mixing up two different expressions.
According to the Cambridge Dctionaary, the expression take it easy measn rest, relax, stay calm.
Take it easy with me
means let's you and I relax together.
You would only use on when specifying a day, for example
Take it easy on Sunday.
The expression that you are probably looking for is go easy on, which means to treat someone in a gentle way, esp. when you want to be or should be more severe
So, if you have done something bad and you want somebody to be lenient with you, you could say
Go easy on me.