This movie's ending left me scratching my head over its meaning, and I watched it two more times...  I was intrigued to the point that it inspired me to make a whole YouTube video series analyzing the hidden themes in movies.  (I also analyzed 
Splinter (2008) here.)
Check it out below!  I teased out some subtle details you may have missed, even on repeat viewings & I pitch my own theory that nothing supernatural happens in The Babadook and everything in this movie can be explained by natural means:
The Babadook SECRETS REVEALED!--Video Analysis
What did you think of the movie?  What's your theory on the Babadook's identity or origins?