It's also a possibility that he is also suffering (still in love with his ex), that's why he's depressed.
i would be afraid to date someone who just broke up with someone, thinking im his rebound.
There's nothing wrong with being depressed, but there's something wrong with crying over your ex while with someone else.
He can feel bad about his ex, but continue dating you, the point that he stopped....is a red flag that something is going on. Run!!