sit up with (one)
To stay awake past the usual time to go to sleep in order to care for one or keep one company. My daughter kept vomiting, so I had to sit up with her through the night.
sit up with someone
to stay with someone through the night, especially with a sick or troubled person or with someone who is waiting for something. I had to sit up with my younger sister when she was ill. I sat up with Bill while he waited for an overseas telephone call.