weight
I'm afraid my opinion doesn't carry any weight with my boss.
The Olympic symbol carries a lot of weight.
His words would carry more weight if he did himself what he advised others to do.
Do you think that's a message that carries any weight with the authorities there?

SMART Vocabulary: related words and phrases

Affecting and influencing
across-the-board
affect
applicability
be/fall under someone's influence/spellidiom
bear on something
carry
colour
ear
inspiration
instrumental
instrumentality
instrumentally
interinfluence
pen
rail
spill
spill over
sportswashing
start (something) off
talismanic

carry weight | American Dictionary

carry weight

idiom
to be considered serious and important enough to influence other people:
The Senator's opinion carries a lot of weight in Congress.