I had the same problem with my ds who was a chunky little guy. But have found that not using a snappy at that age was much easier and helped the problem.
I LOVED the bikini twist on him once he went up to the regular or premium size. I got a much comfier fit on him.
Also you may have to look at the clothes they are wearing. There are a lot of baby clothes these days that are slim fitting and don't fit well around cloth diapers. A lot of pants (usually cords or jeans would cut my ds at the thighs and he couldn't sit down. Probably not a big issue at 3 weeks since most of their clothes are roomy and soft but something to think about as they get bigger.