THESAURUS
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
ROGET THESAURUS
carry weight
Importance
VB
be important, be somebody, be something, import, signify, matter, boot, be an object,
carry weight, make a figure, be in the ascendant, come to the front, lead the way, take the lead, play first fiddle, throw all else into the shade, lie at the root of, deserve notice, merit notice, be worthy of notice, be worthy of regard, be worthy of consideration, attach importance to, ascribe importance to, give importance to, value, care for, set store upon, set store by, mark, mark with a white stone, underline, write in italics, put in italics, print in italics, print in capitals, print in large letters, put in large type, put in letters, of gold, accentuate, emphasize, lay stress on, make a fuss about, make a fuss over, make a stir about, make a piece of work about, make much ado about, make much ado of, make much of.
Influence
VB
have influence, be influential,
carry weight, weigh, tell, have a hold upon, magnetize, bear upon, gain a footing, work upon, take root, take hold, strike root in, run through, pervade, prevail, dominate, predominate, out weigh, over weigh, over-ride, over-bear, gain head, rage, be rife, spread like wildfire, have the upper hand, get the upper hand, gain the upper hand, have full play, get full play, gain full play, be recognized, be listened to, make one's voice heard, gain a hearing, play a part, play a leading part, play a leading part in, take the lead, pull the strings, turn the scale, throw one's weight into the scale, set the fashion, lead the dance.
Evidence
VB
be evidence, evince, show, betoken, tell of, indicate, imply, involve, argue, bespeak, breathe, have weight,
carry weight, tell, speak volumes, speak for itself, rest upon, depend upon, repose on, bear witness, give evidence, testify, depose, witness, vouch for, sign, seal, undersign, set one's hand and seal, sign and seal, deliver as one's act and deed, certify, attest, acknowledge, make absolute, confirm, prove (demonstrate), indorse, countersign, corroborate, support, ratify, bear out, uphold, warrant, adduce, attest, cite, quote, refer to, appeal to, call, call to witness, bring forward, bring into court, allege, plead, produce witnesses, confront witnesses, place into evidence, mark into evidence, collect evidence, bring together evidence, rake up evidence, experiment, have a case, make out a case, establish, authenticate, substantiate, verify, make good, quote chapter and verse, bring home to, bring to book.