This site: http://www.intuitor.com/physics_test/exp… claims that it is not the force of gravity, but the force of surfaces (like the floor or sofa) pushing on my body that gives me a sensation of weight. If this is the case, why does my arm feel heavy when I hold it out (there is nothing pushing on my arm)? Or is it the sensation of the muscles in my body pulling on the bone which create the sense of "heaviness"?
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yes it is the forces exerted by your muscles that gives you the sensation of overcoming the force of gravity.
Another way to think about this is to consider someone in a spacecraft orbiting the earth in free-fall. They are still experiencing the force of gravity roughly similar to someone at the earth's surface, but because their body and arms are falling at the same rate they do not need to exert effort to keep their arms held out, and no surface is required to keep them upright or floating as the craft is also falling, hence they experience weightlessness (although it is only a feeling of having no weight, as in reality they do still have weight in the physics definition of the term).
Another way to think about this is to consider someone in a spacecraft orbiting the earth in free-fall. They are still experiencing the force of gravity roughly similar to someone at the earth's surface, but because their body and arms are falling at the same rate they do not need to exert effort to keep their arms held out, and no surface is required to keep them upright or floating as the craft is also falling, hence they experience weightlessness (although it is only a feeling of having no weight, as in reality they do still have weight in the physics definition of the term).