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]
(..) This is your legacy. A new generation of weapons with this at its heart. Weapons that will help steer the world back on course, put the balance of power in our hands. The right hands. I wish you could've seen my prototype. It's not as... Well, not as conservative as yours. (..)2008 Iron Man