I think it is normal to want to be close to mummy, he has been tucked up inside you for 9 months.
There's a theory of the 'fourth trimester', which suggests that babies are still very dependent on physical closeness, warmth, and so on. It really made sense with both my LOs, but personality made a big difference. 'Touchy' LO1 let us know how much he wanted to be held, wouldn't go in a push-chair, had to have a sling, etc etc. I ended up going much the same route with 'Angel' LO2 who just loved being cuddled
It was lovely with both of them though. Bear in mind, he's still very tiny, so don't panic about creating habits.
Congratulations and hugs!