carry an amount of weight
carry (an amount of) weight
To wield (some amount of) importance or influence. Due to your status, your remarks carry a lot of weight, so I encourage you to speak out on this issue—people might finally start taking it seriously. Without research to support these claims, I'm afraid they don't carry much weight. The name of the company still carries weight in this industry, even if it has been out of the spotlight for the last few years.
Farlex Dictionary of Idioms. © 2022 Farlex, Inc, all rights reserved.
carry (an amount of) weight
tv. to have a degree of influence. Tom carries a lot of weight with the mayor. Ask him.
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.