I ride bikes. If you get into any of the performance two wheel community you will start to encounter weight weenies... the default position of all of them is that the best place to loose weight is in the wheels.
There is several reasons for this. Firstly it is unsprung weight. This means your suspension is not carrying it, but trying to handle it. Suspensions virtually universally work better on sprung weight. Secondly the gyroscopic effect of the wheels gets larger as the wheels get heavier... this leads to harder steering. Finally as the weight of the wheel increases the amount of force needed to accelerate it increases in a non linear fashion (IIRC it is a squared function). All of this means that you need to put a lot more energy into accelerating and decelerating a car. Greater amounts of energy require greater amounts of fuel...
On a side note... it is estimated that the extra load on a sport bike at 100MPH of 1 lb at the wheels is the same as adding 40 lbs on the bike body or on the rider. Bearing in mind that a bike rider combo typically weighs in the 700 lb range, it can be seen that shaving 1 lb of each tire would be seen as similar to a 10% reduction in the overall weight of the bike.