Simple enough....
As most of us know , the reason you do feel your weight at all on the earth is due to the influence of gravity or the attraction (according to Newton) between you and the molten crap at the earths core.
The expression for this force which you feel is given by F=mg , where m is a property of your body called mass , and where g is the acceleration due to gravity which has a value ( on the earth's surface) of 9.81 metres per square second.
At this juncture i must introduce all of you to Newton's third law of motion : Every action has an equal and opposite reaction.You feel this in the recoil of a gun when you fire it and it is also the reason you stay put on the earth's surface and don't sink towards it dark , murky and extremely hot depths.
It is actually precisely for this reason that you feel your weight at all , ie your weight as you perceive it is nothing but the reaction of the ground due to the acceleration due to gravity acting on your body.
In the case of a free fall or when your car moves over a bridge etc.etc. this is exactly what is happening.There is no ground to counteract the force exerted by gravity on your body and hence you feel weightless.
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