Answer
The trajectory of a freely falling body ensures that the pseudo force in the noninertial frame of the airliner cancels out the acceleration due to gravity.
Work Step by Step
The trajectory of a freely falling body follows a parabolic path. The component of velocity perpendicular to gravity is unchanged (ignoring air resistance) and the component of velocity parallel to gravity is accelerated at $g = -9.8m/s^2$.
A person in a frame of reference (the airliner) moving in the trajectory of a body in free fall feels no force in the direction perpendicular to gravity, since the component of velocity in this direction is constant.
However, due to the acceleration of the reference frame in the direction of gravity at $a=g = -9.8m/s^2$ in accordance with the trajectory of a freely falling body, he experiences a pseudo force in the opposite direction with magnitude $F_{pseudo} = ma_{pseudo} = -ma = -mg$. But this is equal and opposite to the force of gravity acting on him $F_{gravity} = mg$. Thus the net force acting on the man $F_{net} = F_{pseudo}+F_{gravity} = 0$.
The man hence feels weightless.
