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when a force acting on a body has equal and opposite reaction then why should the body move at all

According to the third law of motion the action and reaction forces act on two different object and that is why the object moves.
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Even though the action and reaction are equal and opposite, the object moves because these force act on 2 different bodies. So an individual body experience 1 force only. Thus, these forces don't cancel eachother and the object moves.
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it is because of the variation i their masses
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For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects not on a single body.
 
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