One thing that could bring more public attention to the Commonwealth Games is having the events shown on a major international sports channel such as ESPN and some of the major networks that have sports channels like NBC and Fox. These Games always feature major international and succesful athletes that people from all around the world have heard of or have actually seen compete in person.
The Commonwealth Games are widely advertised in the Commonwealth of Nations countries and territories but that is it. If there were more of a push for more international advertising and exposure of the Commonwealth Games the more of a chance that more fans would watch the events and in the end would bring more public attention.
Another thing is that more people are more interested in the regular Olympic Games than the Commonwealth Games. While the Commonwealth Games stages the same events and awards medals to both men and women and has events for paraolympians, it is the regular Olympic Games that garner the more attention. A more widely pushed international ad campaign for the Commonwealth Games would make the competition more relevant.