counterweigh vs fly in the face of

counterweigh

verb
  • To act as counterbalance (against something). 

  • To counterbalance; to balance out. 

fly in the face of

verb
  • To act in a manner highly contrary to; to counteract or contradict. 

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