I don't understand how this can be true if speed changes.No, the speed would not remain constant. It varies with the distance from the earth. As that distance increases, gravitational potential energy goes up and kinetic energy, and thus speed, goes down.
If your speed changes then you accelerate and decelerate or vise versa how come you would not feel any kind of weight.If, on the other hand, you were moving horizontally near the earth, if the only force acting on you were gravity and if your speed were faster or slower than that which would put you in a circular orbit then you would still be in free fall. You would follow an elliptical, parabolic or hyperbolic trajectory.
But you would not feel any kind of weight.