When we are going on an inclined line on a slope on a roller coaster, the chair or the floor exert a force on us to balance the weight due to gravitation of Earth. When the reaction force acts on our feet or our buttocks or back, that pressure and sensation makes us feel the our weight.
When we go through a vertical loop we are going in a circular arc. At the top of the roller coaster (inverted U arc), a force called centripetal force is required to make us go in a circle. This force depends on the speed, the radius of curvature and our mass.
our weight = Normal reaction of the floor/chair + centripetal force
normal reaction of the floor or chair = our weight - centripetal force
So the apparent weight is reduced by the centripetal force. So the contact between our feet or body with the roller coaster becomes very light. So we feel weightlessness.
Also at some points, there is a near free-fall of the persons on a roller coaster. Then the apparent weight we feel = our weight - m * acceleration of the free fall.
So our apparent weight reduces a lot, when we move down a slope with a large acceleration.