"To tip the balance" is a frequently-used idiom. See HERE.
Student or Learner
What does 'tipping balance' mean in this case?
Non profit-educational or personal use tips the balance in favor of fair use.
Tip, here means like 'giving something'? Balance is like bank account balance?
"Tipping the balance" is used in the context of a decision being made. Think of a pair of scales, where each dish weighing down represents a possible outcome of the decision. If something happens which sways the decision one way or another, you can say that the balance is tipped in favour of that outcome. Thence, "tipping the balance". In the context you have given, using copyrighted material for non-profit, education or personal use means that it is more likely that said use will be deemed fair use.
[Not a teacher]