carry weight vs make a difference

carry weight

verb
  • To have influence. 

  • To be handicapped by an extra burden, as when one rides or runs. 

make a difference

verb
  • To be of importance; to matter. 

  • To carry out an action, the result of which is a significant change, or an altered circumstance. 

How often have the words carry weight and make a difference occurred in a corpus of books? (source: Google Ngram Viewer )