Specific gravity is just a ratio of the density of a certain amount of material (jet fuel in this case) to the weight of an equal amount of distilled water at a set temperature. For example, 1 gallon of Jet A at 60 deg. F may weigh 6.78 lbs and a gallon of water weighs 8.35 lbs. When you take 6.78/8.35, you end up with .81. That is your specific gravity of the Jet A sample you took. If you were to add an additive like Prist, which is heavier than Jet A, to the fuel, and still took the identical size sample, the fuel would be slightly heavier per gallon. This would make the SG higher. The reason some people debate the weight of Jet A is because it actually changes. Altitude, temperature, and other atmospheric changes affect the specific weight of the fuel which will affect the SG.

So in your example, your gauges may be calibrated for (or you are multiplying by) a different SG (weight/gal) of fuel than you are being filled with. Often when you pull fuel from an underground tank (cooler, thus more dense and heavier per gallon) and fill your aircraft, the outside air plus the sun will increase the temperature of the fuel causing it to expand, therefore increasing the amount (gallons) of fuel in your tanks. (Understand the weight will stay the same - unless you initially fill full and then when the fuel expands, the extra flows out the vents.) When you get to a higher altitude and the fuel cools and contracts, you will actually have less fuel in your tanks (gallons) but will weight proportionately more.

PS, since the specific gravity will be higher (more dense) at higher altitudes, the fuel is more potent per gallon than at lower, warmer temps. This helps to increase your power while burning less fuel.

Confusing? Let me know