Appropriate register for duct size?
Given a circular 8" duct you are dealing with an airflow area of about 50 sq/in.  You currently have 72 sq/in opening.  I haven't seen a picture of your register - some are not as open as others so it is hard for me to know for sure but... with 72 sq/in opening the air would just dribble out.  

This is fine for a floor vent that is unobstructed by walls and furniture but usually not what you are going for.  You are usually looking to push the air out a few feet out into the room.  A smaller register does this.  Also somewhat closing a register does this - however this could push air at unadvantageous angles and you don't want air hitting walls and furniture.  

Most registers I size are about the same sq/in's as the duct or a little less.  I am looking for the air to be pushed out hard so that it creates airflow in the room.  Big rooms with oversized registers can have hot spots away from the register.  Now the downside of going to small with your register is that it is too loud.  Unless you are severely undersizing your register, the noise is really the only issue.

So a bigger register will not help cool or heat your room better.  Putting the register in a better location and making sure the air is shooting out in an efficient manner and at an efficient angle is key.