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]
(..) - You were the mercenary. Bane is your child. Your heir. An heir to ensure the League of Shadows fulfills its duty to restore balance to civilization. No. You yourself fought the decadence of Gotham for years... with all your strength... all your resources, (..)2012 The Dark Knight Rises
(..) Oh. And the proceeds will go where they should, because I paid for the big fat spread myself. That's very generous o' you. You have to invest if you want to restore balance to the world. Take our clean-energy project. Sometimes the investment doesn't pay off. - I'm sorry. (..)2012 The Dark Knight Rises