While I agree that you shouldn't stress about tire weight, you should know that unusually heavy tire/wheel combinations cause you to have to work a little harder to accelerate. It takes more force to spin up a heavy wheel than a light wheel, like a heavy flywheel on an engine as opposed to a lightened flywheel. If you are used to lightweight wheels and tires, you will notice the difference when moving to something heavier. This also means that once the heavier wheels are up to speed, they have more momentum than lighter wheels.

Added weight on other parts of the bike have a much smaller impact on your ride than heavier wheels or tires, because of the flywheel effect realized by spinning wheels. Most of the tires mentioned above are reasonable in their weight, so you shouldn't have any issues. I have an old set of Innova tires that have rather thick tread on them, and the difference in weight with them is enough to feel when spinning up the wheels. Those tires stay on the shelf for that reason.