Most airlines look for the linear dimensions of the box. That is weight plus height plus depth. I'm a frequent flyer so I skip Southwest, but you should be able to find this on their website. Going over it usually means a fee as does being overweight. Depending how much you're shipping this might not save you a lot. You still have to get everything from the airport to the dorm. Bins are great, but are you taking them back with you? He'd have to store them somewhere.

Good luck.