sway

(noun) controlling influence.

(noun) pitching dangerously to one side. Synonyms: rock, careen, tilt.

(verb) move back and forth or sideways. Synonyms: rock, shake. Examples: "The ship was rocking." "The tall building swayed." "She rocked back and forth on her feet."

(verb) move or walk in a swinging or swaying manner. Synonyms: swing. Example: "He swung back."

(verb) win approval or support for. Synonyms: carry, persuade. Examples: "Carry all before one." "His speech did not sway the voters."

(verb) cause to move back and forth. Synonyms: rock. Examples: "Rock the cradle." "Rock the baby." "The wind swayed the trees gently."