Leaks leaks and more leaks

My son is 5 weeks old. I am trying to get him use to sleeping in his own crib in his room (my room didn’t work out) and it’s been successful kind of…

He does wake me up every 3-4 hours to feed.

But once he is asleep and I place him in his crib..,

1 hour later he cries… I know why.. by the time I get some rest or about to.. he cries..

He is soaked. His diaper leaks.. he uses size 1 . I tried huggies and pampers.. maybe diapers are too big ? But the newborn diapers are too small (facts) he weighs over maybe 9lbs.. he was 8.10 when he was 2 weeks old.. I just don’t know what to do!!! I can’t get any sleep… he doesn’t leak when he is in his swing for his naps. I am tired !! I am tired of the leaks . He’s currently is using huggies and I loved huggies.. I’ve tried pampers. I just want some rest