... 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.
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).