I wondered because it seems like you did get your pup at a very early age - before the ideal , recommended age to go to the new home. Now you are saying that you took the dog to the vet at 7 weeks of age because he had not eaten for a week , that means a pup around 6 weeks of age that had not eaten for a week .
That is an important time in developing the immune system , rapid growth .
When did he get his first vaccination ? Before or after you added him to your home?
Knowing that he was not in prime health I would have held off on giving him the second vaccination "My GSD is now 8 weeks old, he has had 2 of his puppy shots"
Why was your vet so hasty to vaccinate the pup who was not in the best of shape , even if the dog was just blue or depressed from leaving mum-dog and littermates , this is stress which has physical implications . The dog was not well . The vet very well could have said take your pup home Mrs and feed him this ... whatever, whatever, lets get him on his feet, a bit of meat on his ribs , keep him home and then see me in two weeks for a re-evaluation.
You CAN create problems , which will show themselves later on in life .
from Dr Dodd's - "Puppies receive antibodies through their mother’s milk. This natural
protection can last 8-14 weeks. Puppies & kittens should NOT be
vaccinated at LESS than 8 weeks. Maternal immunity will neutralize the
vaccine and little protection (0-38%) will be produced. Vaccination at
6 weeks will, however, delay the timing of the first highly effective
vaccine. Vaccinations given 2 weeks
apart suppress rather than stimulate the immune system. A series of
vaccinations is given starting at 8 weeks and given 3-4 weeks apart up
to 16 weeks of age. Another vaccination given sometime after 6 months
of age (usually at 1 year 4 months) will provide lifetime immunity."
Ideally the first one should be given at about 9 to 10 weeks
Dr. Jean Dodds' Pet Health Resource Blog | Dr. Dodds' 2012 Canine Vaccination Protocol
the second about five weeks later.
There are many kennels which select one pup , the strongest one, vaccinate that pup as per protocol , put that pup back in with the others and the others will have a mild exposure which triggers their immune response.
Titers can be done to monitor the dogs immune response and vaccinations can be given when called for , and you can be selective and only vaccinate for the portion that you need to "boost".
There are many people doing this for their children .
It is NOT about economy but in reducing risk .
I took the time because I care .