I know you aren't talking about a shortage of money but that was the case of my teenagers running out of gasoline. I tried to drill it into them when they called me to come get them from wherever because the tank was empty. It costs exactly the same to drive with a full tank as it does with an eighth of a tank (or a sixteenth).
Nope.
Fill your trunk with sand and check your mileage.
Weight is weight; whether it is sand or gas.
Also; the slight among of gas used to actually drive INTO the gas station does add up; and many folks will NOT turn off the engine, preferring to keep the car either warm in the winter or cool in the summer.