The phrase "mean mug" is usually found in literature.The word "mug" in this context is a slang word for face and the phrase "mean mug" is generally meant to convey a description of a face as cruel,...
It means that the person is as important to you as is the entire world. You care for them as much or more than all of the wealth in the world. That they are your world and your interests revolve...
"It means just what it sounds like - something doesn't mean anything. It is not a grammatically correct idiom, which is why it probably sounds odd. The original usage was from a song "Don't mean a...