https://en.wikipedia.org/wiki/Drop_tube -- https://en.wikipedia.org/wiki/Reduced-gravity_aircraft -- https://en.wikipedia.org/wiki/Free_fall
Our brain is used to gravity. That is why weightlessness feels weird.
But falling and weightlessness are indistinguishable to your brain. They are exactly the same thing.
So, if all the gravity around you suddenly disappeared, your brain would initially tell you that you are falling.
Only after some time would you convince yourself that, "No, I'm not falling... Gravity just disappeared. I'm just weightless."
The opposite of falling is accelerating, and you feel acceleration. A rocket rocketing in an empty universe would feel the same as a rocket rocketing in orbit would feel the same as a rocket just sitting around on Earth. Wait, that last one's different...
We happen to live most of lives in a somewhat exceptional case of constant acceleration (with respect to falling). The ground below our feet has gotten us pretty used to acceleration. But, if you jump, you'll feel like falling too!
Weightlessness only feels weird because we rarely feel it.
If you were suddenly in empty space (e.g. in an area with zero intrinsic acceleration), you would feel like you are falling.
Because the feeling of falling is actually the feeling of NOT having the constant gravity (i.e. acceleration) you're used to.
If you were born in weightlessness, gravity would be the strange feeling (cue Bane saying, "you only adopted weightlessness, I was born in it").