The textbook definition of “weight” is the force that gravity asserts upon you. By this definition, as you free fall, you very much still have weight.
However, in common speech, when we say “weightlessness”, we are referring to those astronauts floating around in the space station. By this definition, the feeling that you get as you free fall and the weightlessness experienced by the astronauts are exactly the same thing — the astronauts are falling towards Earth just like you, except that they are traveling sideways so fast, and because the Earth’s surface is curved, that they never actually hit the ground.
So yes, that is weightlessness that you feel. But it is not because weight is relative. Instead, it’s because “weightlessness” isn’t really related to “weight”.
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