That is less than half the speed required to reach orbit. Even so, it is enough to carry the rocket to a maximum height of 720 kilometres before it falls back to Earth. The stone is only weightless for a few seconds, of course, and air resistance provides a force that nudges it out of a true, free-fall parabola.
Scientists prefer the term microgravity to weightlessness or zero-g because it is more accurate.
There is always some residual acceleration force, although in a good microgravity environment it is a very small fraction of the full 1-g gravity that gives us our weight on the surface of the Earth. Incidentally, microgravity does not mean that gravity itself has been reduced, only gravity's effects. In most cases, the reduction in gravitational effect is temporary. Like the astronaut, you are falling freely under the acceleration of gravity. For a more prolonged and less fatal encounter with microgravity, you could arrange a trip on the ESA's Airbus 300 Zero-G or on NASA's 'vomit comet'.