If your HVAC (heating and cooling system) was properly designed, it was designed with all the registers open. The grill sizes are also taken into account for proper sizing and velocity, for comfort and efficiency.
Closing registers causes static pressure and decreases the system's performance. It does seem counterintuitive, but closing your vents will not save you money and will hurt your system. The system will run louder and the blower will have to work harder, which can reduce the durability and result in having to replace the system.That can be expensive.