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]
(..) That's great. M.J., let's go! Wait. Thanks! Parker, let's do it. We've solved the horizon glide and the multi-G balance issues. I've already seen the glider. That's not what I'm here for. General Slocum, good to see you again. Mr. Balkan, Mr. Fargas. - Norman. (..)2002 Spider-Man