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]
(..) carrying? You're still too heavy. Just this. What is that, a brick? All this time you've had a brick? Why do you have that? Well, to balance out the weight from the other one. You have two bricks? Yes! Throw them down immediately! (..)2012 The Dictator