Originally posted by McLake
1) "g" down balances "a" up so no resultant force, so no weight.
I think (?) weightless is where there is no reaction force to balance our weight.
If our weight (the "g" down) is balanced, we don't feel weightless. Think about it: standing on the earth, we feel a "g" down, and the ground gives an "a" up to balance it - no resultant force, but we don't feel weightless.
I think you said what I said in the second point:
Originally posted by McLake
2) To feel weight a normal force must be acting on you. If "a" = "g" there is no normal force, so no weight ...
By the way, "weightlessness" is a misleading name. We can have weight provided by the Earth and still feel "weightless" (like what happens with astronauts in a satellite), but that's 'coz there's no reaction force to our weight. "Weightlessness" should be called "NoReactionForceNess"