I remember the 5-6 weeks mark being particularly cranky, growth spurt kind of time, for us it was much worse then the 3 week growth spurt. Maybe its somthing like that?

have/would you consider using a less rigid sling (like a ring sling, babsling, hug a bub) and letting him sleep in there during the day if that helps? It would enable his weight to be far more evenly distributed (esp the HAB) and he'd feela lot less heavy.