This is because what we feel as weight is not caused by the force of gravity pulling us down. It's caused by the force of the floor (or the chair, or the roller coaster seat) pushing against our body and holding us up. When we fall – when there is nothing to hold us up – we're weightless.

You feel weightless on a drop tower because you—and the seat you are sitting in—are in a state of free fall, where the only force acting upon you is gravity. Under normal circumstances, you "feel" your weight because the ground (or a chair) pushes back against you with an equal and opposite "normal force." This sensation of being pushed is what your brain interprets as weight. When a drop tower releases, it accelerates you downward at approximately 9.8 m/s2, which is the acceleration due to gravity (g). Because the seat is falling at the same rate as your body, it stops pushing back against you. Without that "normal force" to resist gravity, your internal organs slightly shift, and your body experiences the sensation of "apparent weightlessness." This is the same principle that allows astronauts on the International Space Station to float; they aren't in a place without gravity, but rather they are in a constant state of free fall around the Earth. The "stomach-flip" you feel is your body's vestibular system reacting to this sudden removal of the support force it relies on for balance.