He's trying to keep his work life and his family life 'in balance'. = He's trying to keep his work life 'in balance with' his family life. [=he's trying to give a proper of amount of time and attention to both his work life and his family life]
The discount 'balances out' the shipping charge. = The discount and the shipping charge 'balance' each other 'out'. [=the shipping charge and the discount together equal zero]
He needs to achieve/create/strike a better 'balance' between his work life and his family life. [=he needs to spend less time at work and more time with his family]
(..) Would be pulling on all the planets Harder than the sun does. And so it's just gonna totally disrupt The gravitational balance of the solar system. Narrator: The black hole would literally tear planets from their orbits And smash them into each other. It's just an epic disaster. (..)2010 TvShow: How the Universe Works Title: Black Holes Season: 1 Episode 2