a). Gravity does change across the surface of the Earth and throughout its atmosphere, due to several effects. First, there is the variation of gravity with latitude that you alluded to: you weigh about 0.5% more at the poles than on the equator. ... Second, gravity does indeed change with altitude.
b). That's because the planets weigh different amounts, and therefore the force of gravity is different from planet to planet. For example, if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury. That's because Mercury weighs less than Earth, and therefore its gravity would pull less on your body.