The biggest factor that effects the polarizability of a substance is the size of the material. Larger molecules, atoms, or ions are more polarizable than smaller objects.

Compare F₂ and I₂; the Lewis structures for each are drawn below.

The atomic numbers are included to remind
us of the number of core electrons.

To induce a dipole some of the electrons must be attracted to (or repelled by) another charge.

Which element more strongly attracts it electrons, I or F?

The electrons of which element will be easier attract?

Since iodine's electrons are not as strongly attracted to the nucleus the electrons will be more easily pulled away from the nucleus. Because the electrons are moved with greater ease a dipole forms more easily. Iodine is more polarizable than flourine (this is true for both the individual elements and the diatomic molecules).