Why to astronauts appear weightless while they are filmed performing activities inside the orbiting space shuttle?

They are high enough above the earth's surface that they have escaped the pull of earth's gravity.

The space shuttle has anti-gravity devices on it that allow the astronauts to float inside it.

The astronauts are falling at the same rate as the space shuttle as it orbits around earth.

Orbiting objects do not experience any gravity.

an astronaut is under the gravitational force of any object nearby that has mass.

Answer: The astronauts are falling at the same rate as the space shuttle as it orbits around earth

The astronauts seem to float because they are in free fall just like the spacecraft.

However, although they are constantly falling on the Earth, they do not fall because the ship orbits at a sufficient speed (in the same direction of rotation of the Earth) so that the centrifugal force is balanced with the Earth's gravitational pull.

In other words:

The spaccraft and the astronauts are in free fall but the Earth's surface will never be reached as long as they does not decrease the speed.

Then, as they accelerate toward Earth (regardless of their mass), it curves beneath them and never comes close.

That's why astronauts, having the same acceleration as the spacecraft, feel weightless and see themselves floating.