This idiom or expression has to do with:

Having a powerful punch.
Having a lot of power or influence.

Hey, your kid brother really packs a punch. I’m still dizzy!

This idiom or expression has to do with:

Having influence, importance, or significance.

A. I’m still looking for a job, but I haven’t found one.
B. Ask your father to help you. He carries a lot of weight around here.