Why metallic ions are larger in size as compared to non metallic ions?

As a matter of fact, not all metallic ions happen to be larger than non-metallic ions. Ionic size depends on the charge of the ion, the number of electrons in the orbitals.

Ionic size of any Group increase down the group, metallic or non metallic.
Ionic size decreases along periods, until the ions formed are negative (most non metallic ions) where the ionic size suddenly increases. After that increase, the ionic size decrease again.

The more electron shells, the larger the ion. has 2 electron shells, but has 3 electron shells. Therefore, in salt, the sodium ion is smaller than the chloride ion.

Metals lose electrons when they become positive ions, hence, their ionic size is smaller than their atomic size. Non metals gain electrons when they become negative ions, hence, their ionic size is larger than their atomic size.

I hope it helped! :)