Why is acceleration due to gravity at higher altitude and less altitude different. Why?

As Newton's law stated, if you are closer the attractive mass, the gravity force (and acceleration) is bigger; if you are distant from the mass, the force is small. This principle applies to the Earth's gravity field: if you consider all the earth's mass concentrated in its center, when you are in a mountain the gravity force would be smaller than the force when you are at sea level. Of course the mass of the mountain also contributes in this balance. But, in general, we have a mean decrease of 0.3086 x 10-3 cm/s2 per meter of altitude (this is what we call normal gravity gradient), i. e., if you stand in a place that is 1 m higher than the mean sea level, the gravity acceleration will decrease 0.3086 x 10-3 cm/s2 (sorry about the superscript/subscript, but I think you can understand). The gravity changes in different places in the world because different places have different mass distribution in subsurface and different heights above sea level. The combination of these two factors generates the change in the gravity value (gravity here meaning gravity acceleration). The centrifugal force also adds a component in this problem. In fact, in geophysics, gravity is a fundamental method of investigating the Earth. Measuring the gravity acceleration in several places you can determine how the mass is distributed within the Earth.