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Polarizability increases the molecule size increases because this means that the electron shells increase and therefore the size of the electron cloud increases. The valence electrons get further away from the nucleus and experience weaker effective nuclear charge thus making them more easily distorted (polarizable).
Larger molecules are more polarizable because the electrons in the outer shell are easier to take away. This is because they are "shielded" from the nucleus by the other electrons so they can be taken away from the atom easier.
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