sway

controlling influence

pitching dangerously to one side

move back and forth or sideways; "the ship was rocking"; "the tall building swayed"; "She rocked back and forth on her feet"

move or walk in a swinging or swaying manner; "He swung back"

win 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"; "the wind swayed the trees gently"