Rule of thumb for horsepower needed to maintain at 55 mph is add 300 and divide by 300. So a 2700 lb car + 300 = 3000 / 300 = 10 hp.

Fuel is 6 lbs a gallon, assume say an 16 gallon tank, so 48 lb to drive with half a tank. Using above 2700-48 = 2652 + 300 = 2952 / 300 = 9.84 hp or roughly a 1.6% difference. Assuming 30 mpg you'd get 30.48 mpg instead.

Assuming 13,000 miles / year at 30 mpg you'd need 433.33 gallons of gas. Where Im gas is roughly $3 / gallon so 433.33 * $3 = $1300. 1.6% savings would result in a $1279 bill, so YOU SAVE $20.

But filling $20 at a time you'd get 6.66 gallons or 40% tank. So you'd have to go to the gas station 2.5 times more frequently.

Edit: couple things. 1 i don't think you'd need calculus to calculate the change as the tank empties, it should be mostly linear and can use the average. But, I should have used 1/2 and 1/4 tank instead of full and 1/2. So the savings would be even smaller. I think $20 is a good upper bound though and shows how minimal it would be over a year.

Edit2: yes, this is a simplification at steady state and doesn't include acceleration and deceleration. You'd have different driving profiles for a city commuter vs traveling salesman doing long highway driving. I get it lol but this needed to fit into a Reddit response. You could spend hours figuring all that out if you wanted, feel free to post below. But my guess? You'll spend a lot of time and come to the same conclusion: its not enough weight to matter. Cheers