Yup a case will make it feel heavier.
It's not just a matter of pure weight, but leverage as well. The iPad mini has a shorter leverage distance from where you hold it (center of mass), but if that mass increases, so will the leverage. Also if you hold the iPad Air with 2 hands, then it's the perpendicular distance to the center of mass rather than the diagonal that forms the leverage, which will make it feel lighter.