Please let me "weigh" in. I was always taught some wheels/tires (and while many think only of balancing tires, it is important to remember you're balancing both) will need weights on front and back to achieve proper results. Using weights on both sides of the wheel is known as dynamic balancing. Normally wheel covers will not interfere with wheel weights although if you use baby moons without trim rings, you'll see the weights. As buckshot mentioned, the machine will let you know. If you want the smoothest ride, the highest fuel economy and the longest life out of your tires, it is mandatory that you get your wheels/tires balanced as perfectly as possible and it is important to have them re-balanced every 10,000 miles or so. I was also taught to take the assembly off, mount it again in a different orientation and spin it another time to see what happens. Almost no shop does that today. These machines are not always exact and if the wheel/tire assembly is cocked just a bit when mounted on the balancer it can throw the results off. Is it really that important? Well, out of balance wheels/tires require a lot more effort to turn, especially at speeds over 40 mph. That will reduce your gas mileage. And out of balance wheels/tires will wear out a lot faster. One more thing: if when buying tires you see criticism that they pick up and hold pieces of gravel, don't buy those. They won't last as long and they'll cost you more in gas spending...because they'll forever be running out of balance. Any weight at the outside edge of your tire will cause a more dramatic out of balance effect. If you want a really dramatic example of this, on your lawnmower blade there probably is a hole drilled very near the ends...most of them have these although I don't know why (usually it is about 1/8 inch or so). Put a small screw and nut in one of those holes and start your mower.