Baby leaking out of diaper

My son was born on the 13th, he was 5lbs 14oz. His pedi appointment was Monday and she said he was now 6lbs 2oz. He’s in newborn diapers and it seems he keeps leaking out of his diaper if would be wet on the side of his clothes. He’ll wake up crying cause he peed. I tried Huggies and pampers but still pees to his clothes.