Sway when the car is not loaded?
Remember, your dolly has no suspension at all. It relies on the cars suspension when loaded. When not loaded a dolly spends as much time bouncing up in the air as it does on the road. It bounces just like a basket ball. Sway might be caused by uneven air pressure in the tires or it might be just how it is landing & bouncing.
My dolly had instruction to avoid towing unloaded but if you had to then lower the tire air pressure. I forget the recommended unloaded pressure but it was so low the tires felt soft.