Being small is definatly not a reason to give extra vaccinations and no veterinarians practice this as far as I know, if anything it's more the opposite with tiny pups. I'd say he's probably had enough vaccines; at one point in the list I think you said they did 3 within 1 month's time frame? that's way too frequent. I'd tell them thanks for the help but you'll be going to your licenced veterinarian from now on. And as someone else said, make sure you take all the records of the vaccines and deworming to your vet. It's not about how much vaccine they are given, it's about building the resistence up in their system over a period of time, age and timing is what's important, not quantity. So glad to hear he's feeling better
