If you are worried about his health make sure you get him checked by your vet. He will need his vaccinations and check up anyway. However, it is normal for puppies to produce small amounts of urine often as they only have little bladders. Just keep popping him outside every hour or so especially when he starting sniffing about. Don’t make a big fuss the association between the substrate he goes on and the relief of urinating is reward in its self and toilet training will happen in time. If you begin to get cross with him he will start to do it when you are not looking. Just remain calm, if he begins to urinate, pick him up and put him where you want him to go. If this is paper or training pads begin to move these over time closer and closer to the door.
All the best
Rosie Barclay.