Why did Roy let Deckard live?

This is a difficult philosophical question.

We, the audience, are asked to judge Roy's motivations from observing his actions. And the fact that there are so many differing versions of this movie makes this a somewhat more than usually difficult thing to do.

Nevertheless, my opinion is that Roy, and the other replicants, long to be human. It seems to me that Ridley Scott is telling us that they are not merely struggling to gain more life, but are actually seeking a way to become fully human; something which, of course, includes a longer lifespan.

My take on Roy is that in saving Deckard's life he is demonstrating to the audience that he is psychologically already human, in that he is acting in the way a human would act.

Whether Deckard, who in one edit subsequently kills Roy, is morally justified in doing so - since he owes Roy a debt for saving his life - is a different question. Subtly, Ridley Scott is implying here that Deckard is less human than Roy, to support the theme Scott is fostering that Deckard is actually a replicant.

Thus, Roy lets Deckard live in order to demonstrate that Roy is thinking and behaving like a human; and, in addition, to contrast this with Deckard then killing Roy, thereby showing himself to be less human than Roy.