[Homeslice]

Interesting piece from wikipedia, explaining that we do "feel" the effects of weightlessness:

The technical definition of weight is the mass of the object, multiplied by the acceleration of the g-force acting on an object, but in the opposite direction. Thus, humans experience their own body weight as a result of this supporting force, which results in a normal force applied to a person by the surface of a supporting object, on which the person is standing or sitting. It is the transmission of this reaction force through the human body, and the resultant compression and tension of the body's tissues, that results in the sensation of weight. In the absence of this force, a person would be in free-fall, and would experience weightlessness.

Because of the distribution of mass throughout a person's body, the magnitude of the reaction force varies between a person's feet and head. At any horizontal cross-section of a person's body (as with any column), the size of the compressive force being resisted by the tissues below the cross-section is equal to the weight of the portion of the body above the cross-section. (In the arms, the reaction force is equal to the weight of the portion of the arm below the cross-section, and is a tensile, rather than a compressive, force, just as in a hanging rope.)

Also:

Other significant effects include fluid redistribution (causing the "moon-face" appearance typical of pictures of astronauts in weightlessness)