Weightlessness is what you feel when you are not supported, but are being pulled straight down by gravity and nothiing is stopping that motion.
You will feel it if you jump out of a tree, off a diving board, or jump on a trampoline nice and high. Note that if you are going upward but slowing down, it is the same feeling as falling. You are simply accelerating downward but your initial velocity was up. The vomit comet does exactly the same thing. It heads up, then on the way up points the nose down so that it and everything/one in it is floating free as if they’d been tossed in a big arc - but without the wind resistance of being flung at 500mph.
The Viking boat thing does sometning similar; you are swung up almost vertical, until you come to a stop and fall back. For most of the upper arc you are close to weigtless because your motion is mostly vertical.
Similarly, when you go over the arc and down the really big hill in a roller coaster, you are falling nearly vertical. Of course, the front is being held back by the not-yet-over-the-hump back, which is pulled faster by the ahead-of-the-curve front. (To simplify things)
Terminal velocity (IIRC, usually about 100mph to 120mph for a human) is when you are falling so far that your velocity reaches the point where the pull of gravity is approximately equal to wind resistance. Unless you are skydiving or scored a really good acid, or that other mountain climber was lying about being your friend, you will never experience this. (Or it could be one of those wing suits in the wind shaft rides…)
Of course, if you are accelerating downward at some point you must stop - either by going “splat”, or by slowing down, or by turning direction like a roller coaster to the horizontal 9and then up again?) If you are slowing down or turning, you will experience extra forces over and above the pull of gravity.
Several things are at work; as mentioned, the feeling in your stomach that it does not need to work to hold your guts up, they aren’t pushing down any more; there’s the motion sense in your inner ear (tiny hairs being moved by a ring of fluid) that tell you if there is change in your movement; never underestimate the value of visual cues, and our instinctive fear of heights or the panic of being in a risky position.