In the classic Simpsons episode "Deep Space Homer," Homer goes to space aboard the space shuttle. While in orbit, Homer experiences realistic weightlessness. While Homer's flight (and the flight of his potato chips and ant overlords) is accurate, your ideas about why Homer and real astronauts are weightless in orbit might not be.
The farther you get from Earth, the less gravity affects you. However, in an Earth orbit, this reduction of gravity is minimal, reducing gravitational force by roughly 10 percent. So an absence of gravity can't explain astronauts and Homer floating around, seemingly weightless.
So what makes Homer float? Free fall. When you're on Earth, you never experience gravity directly. It is a force that acts at a distance, and it's impossible to feel. You only feel contact forces, like a dodgeball hitting you in the shoulder, or the ground pushing up against your feet (which we've learned is called the normal force). If you could somehow eliminate all the contact force, you would experience a feeling of weightlessness, even though your actual weight and the actual gravitational force acting on you remain the same. You get a glimpse of this on a roller coaster as it goes over a sharp rise. In an orbital vehicle, it's as if the astronauts are constantly going over the top of that roller coaster. They're falling, but the space shuttle is also falling away from them, in a constant perpetual free fall around Earth. With no contact forces, they don't experience their own weight. They feel (and appear) weightless.