He is not being stubborn! He just wants to lay in bed with Jyn, this is not a hard task! If he goes back to bed he'll just be thinking about the two of them, so he might as well stay here where he can watch them instead.

"You can hold her as much as you like. I can share with you." As though Jyn hasn't already had more baby time than almost all their other friends. "She is very warm, especially at night."

Jyn just can't hold her all night. She has a baby schedule to keep!