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]
(..) Excuse me. I am fine. Vanessa you know what this means? All honey is now up to the bees, now we no longer have to work so hard all the time. This is a onheilige schenderij of the balance of nature, Benson ... Get still regret. Barry, how much honey you think that is? - Wait, one person at a time. (..)2007 Bee Movie