WordNet (r) 3.0 (2006):

carry weight
    v 1: have influence to a specified degree; "Her opinion carries
         a lot of weight"

Moby Thesaurus II by Grady Ward, 1.0:

36 Moby Thesaurus words for "carry weight":
   amount to something, balance, be featured, be heavy,
   be influential, be persuasive, be prominent, be somebody,
   be something, count, counterbalance, cut ice, cut some ice,
   get top billing, have an in, have full play, have influence,
   have personality, have pull, have weight, heft, hold the scales,
   import, lie heavy, matter, signify, stand out, star,
   strike a balance, tell, tip the scales, weigh, weigh heavy,
   weigh in, weigh out, weight