For every action, there is an equal and opposite reaction.
This means that when you stand on the Earth, you exert a downward force on it (your weight). Simultaneously, the Earth exerts an equal and opposite upward force on you, preventing you from falling through the ground.
However, the effects of these forces are very different:
* You feel the force of gravity pulling you down.
* The Earth doesn't noticeably move because it's so much more massive.
Think of it like this: if you push a wall, you exert a force on the wall. The wall also exerts an equal and opposite force on you. You might feel the wall pushing back, but the wall doesn't move because it's much more massive than you.