What you feel as 'weight' isn't exactly the gravity, but the force which acts on your body to counter the gravity. When you're standing on the ground, gravity acts in vertically downward direction. To counter this, normal force acts in the vertically upward direction which gives you the feeling of weight. During free fall, the only force acting on the body is the force due to gravity which is acting downwards. As there is no normal force acting upward, it feels weightlessness.