Thanks so much, everyone! I have been waiting 2-3 hours before offering another feeding to him and he seems to be much happier with this arrangement! I'm glad to know, though, that your little ones eat really fast too, because he is definitely done within a few minutes. I usually offer one side per feed, since he hasn't shown any interest in the other in months.
I think I'm just a little nervous because at his last doctor's appointment he had gone down from 90% for weight to 75%, while staying at 90% for height - although the doctor assured me this was completely fine for a breastfed baby of his age. But I always like the extra reassurances from other mamas!