sway

The act of swaying; a swaying motion; a swing or sweep of a weapon.

A rocking or swinging motion.

"The old song caused a little sway in everyone in the room."

Influence, weight, or authority that inclines to one side

"I doubt I'll hold much sway with someone so powerful."

To move or swing from side to side; or backward and forward; to rock.

"sway to the music;  The trees swayed in the breeze."

To move or wield with the hand; to swing; to wield.

"to sway the sceptre"

To influence or direct by power, authority, persuasion, or by moral force; to rule; to govern; to guide. Compare persuade.

"Do you think you can sway their decision?"