counterweigh vs overbalance

counterweigh

verb
  • To act as counterbalance (against something). 

  • To counterbalance; to balance out. 

overbalance

verb
  • To throw (someone or something) off balance; to cause to capsize. 

  • To lose one's balance; to fall over. 

  • To be more important than; to outweigh. 

  • To cause an imbalance in (something) by means of excess weight or numbers. 

noun
  • Excess of weight or value; something more than an equivalent. 

How often have the words counterweigh and overbalance occurred in a corpus of books? (source: Google Ngram Viewer )