What they are getting at is that gravity is not a force so much as your mass trying to travel in a straight line through curved spacetime. The weight you feel is because the surface of the earth is in your way.

Get into low earth orbit and that straight path has you going in apparent circles around the planet. You are very much within the earth’s gravity but you don’t feel “weight” because the surface of the earth is no longer blocking your path. You still have mass and inertia and all that, of course.