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 simply walk up behind them and stab them in the heart. - I am gonna stop you. - You never did learn... ...to mind your surroundings. Justice is balance. You burned my house and left me for dead. Consider us even. No one comes out. Make sure. GORDON: (..)2005 Batman Begins
(..) We sacked Rome. Loaded trade ships with plague rats. Burned London to the ground. Every time a civilization reaches the pinnacle of its decadence... ...we return to restore the balance. Gotham isn't beyond saving. Give me more time. There are good people here. You're defending a city so corrupt... (..)2005 Batman Begins