Fuel gauges are discussed here:
8 Gadgets That Lie to You Every Day | Cracked.com
In the last fifteen years, I believe that is the second comment I have read about only partially filling the tank in order to save gas. One gallon of gas weighs 6.073 pounds (
Gasoline - Wikipedia, the free encyclopedia), so if I only half-filled my 11.9-gallon tank, I would shed 36.134 pounds. My Civic weighs 2,519 pounds, so I would reduce the weight by 1.43%. The general rule of thumb is that for every 2% of weight you lose, you increase fuel economy 1%, so that would be ≈ 0.715%, and a 50 MPG tank would become 50.36.
Of course, we do plenty of modifications with smaller results.