That's the question...somehow I doubt that he was just overwhelmed by a bad concience...I think if that had been the case, it would have been almost impossible for him to go on doing the same thing for different reasons.
May be DD just came to forgive and forget Snape's past - give him another chance?
That is actually one theing I meant to question with this thread.
First, Snape kills in the name of Voldemort, then he does the same thing for Dumbledore. See what light that casts on DD?