counterbalance vs tip the scales at

counterbalance

verb
  • To apply weight in order to balance an opposing weight. 

  • To match or equal in effect when applying opposing force 

noun
  • A weight that is put in opposition to an equal weight so it keeps that in balance. 

  • A force or influence that balances, checks or limits an opposite one. 

tip the scales at

verb
  • To weigh in at; to weigh. 

How often have the words counterbalance and tip the scales at occurred in a corpus of books? (source: Google Ngram Viewer )