An object in free fall accelerates towards the Earth at a acceleration equal to $g$ (the accleration due to gravity). Now if we ignore the air resistance, why do we feel weightlessness? I could not understand the reason that we could not feel the pulling force that the Earth exerts on the object.
It's because what you feel is distortions to your body's shape. When in free fall, when air resistance is low, every part of your body is accelerating very nearly the same amount. No difference in force between any parts of your body means your body doesn't have to exert any forces to keep its shape, so you don't feel anything.
If the gravitational field changes fast enough, a phenomenon the Earth is big enough to experience called "tidal forces" kicks in, and you very much would feel it. It is tidal forces from the black hole that cause a phenomenon called "speghettification" - when the forces between your top and bottom, or left and right, are big enough to squeeze you down into a stream, like spaghetti.
When in free fall, neglecting air drag, the only force acting on your body is gravity, which is a non contact force, and you feel weightless. In other words the feeling of “weightlessness” is that of not experiencing the sensation of any contact forces. Stand on the ground and you feel the upward contact force of the ground on your feet that opposes and equals the downward force of gravity, $mg$. Since our bodies are not rigid (they are deformable) they will undergo some degree of compression depending on its orientation and the location of the contact force.
The possibility of experiencing tidal forces in free fall has been mentioned. Tidal forces are due to changes in the force of gravity as a function of the distance from the center of mass of the gravitating body. In other words due to a gradient in the force of gravity.
For a person in vertical free fall near the earth, the force of gravity will be greater on the feet than the head, which could theoretically stretch the person. But for the earth the gradient in the gravitational force compared to the dimensions of the body is so small as to be negligible.
To put things into perspective. The acceleration due to gravity at the surface of the earth is about 9.81 m/$s^2$, depending on location. At 40 km above the equator it is about 9.67 m/$s^2$ or a 1.4% difference.
Of course the effect near a massive black hole is a different matter.
Hope this helps.