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]
(..) How can we know that the tank wasn't simply some part of the trick that went wrong? Mr. Cutter, I see your predicament. But Alfred Borden's life hangs in the balance. If you were prepared to disclose the details to me in private, I might be able to judge their relevance to the case. (..)2006 The Prestige