The issue for me here is you baby is only 4wks old. When I read that I thought WTF....I'm sorry if that comes across harsh but your bubs is so new to the world & even if you do cc it's never done at such an early age. I would be very upset at my DH if he suggested that at such an age. Babies at that age usually feed frequently, have lots of wind & many other things, I don't think they should be left to cry.
Unfortunatly the men seem to find it easier to let it be....I don't know why that is. We tried CC once (one day it lasted) & my DH didn't flinch...men pfffft!!
The Science of Parenting....among other great things in that book it outlines the effect on your childs brain when left to cry for long periods & how it can affect them later in life.