Newton's Third Law of Motion and Gravity

Think about it this way: earth's gravity is exeeting a force on you and you are also exerting a force on the earth. Though, since the earth is so massive, it hardly shows any change.

Forces are equal, but masses are very different

For your second question: stand still relative to the ground. Are you accelerating? No. This is due to the normal force cancelling out the gravitational force since it is in equal magnitude. This is the heart of newton's third law

Also, see kartikey's comment to better understand the forces in play while you are standing

... the reaction force so weak or is only my imagination?

The normal force is exactly as strong as the gravity force:

If the normal force acting on some part of your body (e.g. your head) was not exactly the same as the gravity force acting on that part of your body, that part of the body would be accelerated, fall down and sink into the ground.

Why if the normal force acts upward I don't accelerate?

Some body is accelerated if the sum of all forces acting on the body is not zero.

Because the gravity force and the normal force are equal (but have opposite directions), the sum of both forces is zero.

You could also argue: When you are standing on the ground, the gravity force accelerates you downwards and the normal force accelerates you upwards the same time. The sum of both accelerations is zero.

When you don't touch the ground, there is no normal force. For this reason you are accelerated downwards.

EDIT

Newton's Third Law of Motion

It seems to me that you are mixing up the Second and the Third Law:

• The Third Law says that the force dragging the earth into the direction of your body is as strong as the force dragging your body into the direction of the earth.

  Needless to say that a certain force acting on a very light body (for example your body) has a completely different impact than the same force applied to a very large body (for example a huge ship or even a hole planet).

• What you are talking about is the Second law if I understood your question correctly:

  This law implies that the normal force is as strong as the gravity force IF (and that is important) you are not accelerated (and no other forces act on your body).

The gravity and normal force acting on you do not constitute an action-reaction pair for the purposes of Newton's Third Law. Newton's Third Law generally refers to pairs of forces originating from the same source, but acting on different objects, and does not require that the net force on either of the objects be balanced.

In your example, your normal force is briefly stronger than gravity (while you are jumping), causing you to accelerate upwards away from the surface when you jump. The reaction to the Earth's gravity on you is your gravity on the Earth; likewise, the reaction to the Earth's normal force on you is your normal force on the Earth. While you are just standing, these forces balance out, and when you jump, the Earth's mass is much greater than yours so that only your motion is noticeable.

Why the gravity that pushes me on the Earth is so powerful . . . . ..

There is no pushing that you feel, indeed you do not “feel” the force of gravity directly.

When you are standing on the ground all you can feel is the normal force of the ground acting on you.
For example if you are in free fall there is no upwards push on you due to the ground and you cannot “feel” the force of attraction of the Earth, indeed you “feel” weightless.

. . . . . so why gravity is so powerful that keeps me on the surface but the reaction force so weak or is only my imagination?

The normal contact force on you due to the ground can feel “enormous”.
Just imagine what what you might feel if you fall and that results in a broken limb.

So when you stand still in the ground there are two equal magnitude and opposite direction forces on you which are not a Newton third law pair; the upward force on you due to the ground which you “feel” the effect of and the downward force on you due to the gravitational attraction of the Earth which you do not “feel” but “observe” the effect of.

Why if the normal force acts upward I don't accelerate?

The downward force on you due to the gravitational attraction of the Earth has the same magnitude, so the net force on you is zero.