The measurement that is affected by gravity is weight.
Weight is the force exerted by gravity on an object and is calculated as the mass of the object multiplied by the acceleration due to gravity (W = mass × gravity). While mass is a measure of the amount of matter in an object and remains constant regardless of location, weight can change depending on the gravitational pull of the body you're on (e.g., Earth vs. the Moon).
Inertia is related to mass and refers to an object's resistance to changes in its state of motion, and density is defined as mass per unit volume and does not change with gravity either.