It is very normal and I owould suggest just holding him all the time or having him in a sling. Babies need close physical contact with their primary care givers, and the more they have the better, imo.
My baby did this and I gave in. Soon afterwards, by nine weeks, she seemed to realise that night time was different and started to sleep more then. I did nothing except pander to her and hold her nearly all the time. You need a good sling - I hated mine (Wilkinet).