Don't let it haunt on you for too long. You have tried your best to help your friend, and it failed to the end, but you have tried your best.
Life is a learing process. Everybody learned something from this. Hopefully, many years later, you two will meet again and both will laugh at this "event", and laught togther not at each other.
for your friend, what he needs to learn is, to plan ahead, make sure his suitcase size meets the airlines guideline, and if he has to bring that suitcase, then check it, the worst to pay additional fee. No big deal.
For you, what you could learn maybe from now on, is to learn to say "no" sometimes. Actually it is not that much money for him to take a one way taxi to the airport. And if you have to help him, then i would suggest that you drive your own car, with your own registration and insurance, (what if on the way back, you had an accident driving his uninsured car? that is unthinkable). and when you get to the airport, park at the garage and go in to the ticketing with him. Still, it was not a good idea to leave the suitcase behind with you to send later with other people. (other people have their own suitcases to travel with, why burden them, he should carry it himself, or check in).
but you can not undo what have happened. Life is a learning process, everybody learns and grows. We all make mistakes, big and small, nobody was born to be very experienced and mature with everything. So just move on, don't let the guilt haunt you. If you get a chance to talk to him again, explain to him what had happened. If he doesn't buy it, let it be. One day, he will grow up, hopefully.