In reply to Frank the Husky:
The best answer is "it depends"...
On long journeys as more or less constant high speeds the majority unavoidable waste* loss (hence fuel consumption) is spent on friction / air resistance. A small amount of this will be attributable to the weight of the car since air resistance will dominate. A small weight saving might not be noticeable. Typically frictional losses (due to weight) are less than a few percent of the total and a 1% weight saving probably leads to a <0.1% loss saving since the air resistance is dominant and unaffected. You will be better off checking your tyre pressures.
On short journeys it's different - you speed up and use brakes to slow down. The energy used is 1/2 mv^2 so proportional to "m" so if all your fuel goes into acceleration (not air resistance or other losses) and you drive at the same speeds then you will get an "8Kg/mass of car" saving (0.8% as est above).
This is an over estimate (the assumption as "all") because there are other losses but the proportions depend on many assumptions (eg regenerative braking, you keeping to the same speeds / acceleration, other loses) you'll probably not notice.
Now try this again with and extra person (80Kg) and it starts to become measurable at slow speeds. Add 800Kg (van load of crap) and it's noticeable. Add a roof-rack, open your windows, drive with soft tyres etc etc and it makes a difference.
If these things worry you (and they should) keep a well maintained vehicle and drive 10% more slowly, don't race, keep your distance, drive calmly, remove crap from your car and ride a bike - you will make substantial gains. If you can afford it drive a modest small modern vehicle, preferably electric or hybrid.
* here we'll ignore the thermodynamic losses inevitable in a fuel/heat engine