It's a personal choice on vaccinations. My puppy is almost 4 months now and still hasn't had a shot. We are in a more secluded area and don't do the dog park thing. He only hangs out with friends and their well trained and healthy dogs so I'm not worried about him catching anything.
Looking at my records, Freki was 17 LBS at 12 weeks old. He is now 48lbs.
Go easy on his immune system and lay off the shots 'til he gets bigger and more powerful. That is if you want to. I'm no expert so do your research and see if delaying and reducing all the shots may help your puppy grow.
Best of luck!
My GSD is smarter than your honor student.