When an object initially begins free fall, it is affected by its weight - that is to say, the force that is acting on it due to the acceleration due to gravity (on earth, this is 9.81 m/s2). However, in an atmosphere which we have, air resistance plays a progressively increasing role, and acts as drag.
If you draw this on a diagram, you can imagine an arrow pointing down - the magnitude (length) of this arrow never changes, as the force due to gravity changes negligibly in this context. The arrow representing air resistance however, increases in a logarithmic-esque style fashion, until it reaches a maximum - the same as the magnitude of the downwards arrow i.e. weight. This means the weight is effectively cancelled out due to the air resistance, rendering the object technically 'weightless'.
Fact of the day - this is why the military and space agencies use jets to mimic free fall and generate the feeling of weightlessness in the aircraft, to simulate exercises in zero G - slightly more realistic than being underwater!
