"Can you pay the balance today?" We don't say "pay the balance up" on its own. You could say "Can you pay the balance up front?" This works because the expression is "up front."
The second sentence is correct, although it would probably be "Can you pay the sum of money on your account?" because it is referring to a specific amount owed on the account.
"He has a fixation with his height." I am assuming you just made a typo here.
She has a fixation with her weight." This is correct, but it should be noted that "fixation on" is also acceptable for the last 2 sentences.