Definition of sway:
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"