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As the cloud gets larger and easier to distort, it becomes more polarizable as polarizability is defined by how easily the valence electron cloud can be distorted. Dipoles and polarity are characteristics of covalent bonds, and so I'm guessing higher polarizability leads to the bond having some sort of dipole-like characteristics that make it more covalent in nature.
Covalent character just means that instead of one element fully stealing electrons from the other their electron clouds share, not to the extent that covalent bonds share electrons but there is some sharing rather than solely taking electrons. The larger the atomic radii of an element the more easily the electron cloud can become distorted which means that element has a high polarizability and vice versa, elements with a smaller radius have more protons which want to bring in electrons thus they exhibit a high polarizing power. Hope that helps.
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