newborn awake at night after feed- put down or stay up with?

Laura
My 3 week old typically falls asleep after feeding during the night. Occasionally he's awake, nice and wide eyed. Do you put your baby down and let them try to fall asleep on own? Or make sure they are asleep first? I've been up with him now close to an hour and a half, now with hiccups and it's almost 3am. Would love to hear what you would do.