sway
noun
controlling influence
pitching dangerously to one side
verb
move back and forth or sideways
“the ship was rocking”
“the tall building swayed”
move or walk in a swinging or swaying manner
“He swung back”
Synonymsswingwin approval or support for
“Carry all before one”
“His speech did not sway the voters”
cause to move back and forth
“rock the cradle”
“rock the baby”
Synonymsrock
Source: WordNet 3.1, Princeton University