You're right.
But choosing tires (tyres) based on their wight is not a great idea.
Generally speaking, but not always, the lesser quality tires have less weight and the higher quality tires have more weight. What a bummer, eh?
It boils down to the tire's manufacturing. How they use steel belts and the number of steel belts plays a large part in the end weight. The steel belts along with things like wound nylon strips, spirally wound nylon cord, spiral-wrapped jointless nylon caps, spiral wrapped polamide cords and/or aramid reinforcement all play a big roll in determining the end weight. The different and amount of silica tread compounds also changes the weight, but not significantly in comparison to the other factors.
If you want to do tire and/or tire weight comparisons
http://www.tirerack.com/ is a great resource of information.
The bester

way to change (lighten) unsprung wight is to upgrade the brake rotors and calipers along with the wheels to a performance types. Keeping the same stock size, the performance parts will be lighter. Unfortunatly they usually cost more.
BTW.... the Hankook Optimo H426 is one of the lightest tires, weighing in at 21lbs. AND we all know how much we love these. lol