As you descend into the Earth, there is less mass below you and more mass above you, so the NET gravitional force acting on you is less and you weight less than at the surface. When you're at the center of Earth, the amount of mass acting on you is equal in all directions, so you feel no NET force meaning you are weightless.

When you move away from the Earth's center of gravity (ECOG), the amount of Earth's mass does not change but the distance between you and ECOG decreases so you weigh less. You weigh less on the top of Mt Everest, for example, than at sea level at the same latitude. Also, because the Earth spins it bulges at the Equator and flattens at its poles, so when you're at the North or South Pole you weigh more than at a mid-latitude because you're closer to the ECOG, and when you're at the Equator you weigh less because you're further from the ECOG.

When you think you've got that figured out, try to explain why a hide tide happens at Full moon, when the moon is on the side of Earth furthest from the sun, and also at a new moon, when the moon is on the side of Earth clostest to the Sun.