Mmh, interesting... I've never thought about it so far because I always thought Moriarty was so fixated on Sherlock that everything concerned with Sherlock would be more worthy to him than from anybody else because normal people are so boring, so predictable to Moriarty that he simply does not care at all about them. Maybe Sherlock really is the only person who is worth a 'thank you' from him. Or he just made up his mind (because he's sooooo changeable)?

I think Moriarty was thanking Sherlock because Sherlock had finally "proven" that he was Moriarty's equal (although we don't know how, yet).  Moriarty just wanted an adversary worthy of his intellect and attention, and Sherlock had given him that by proving (somehow) that he could beat him.

Whisky wrote:

Only now getting back to this... thank you for your thoughts

Don't think Moriarty was really suicidal at the pool scene - he didn't HAVE to answer that phone, he chose to. It could have ended there if he had let it happen. But at this point, Moriarty is still intrigued by the game.

Moriarty declares Sherlock his equal in the rooftop scene - even more: Sherlock isn't like him but is him. (I get headaches from this choice of wording...) But for Sherlock, Moriarty is his adversary. Moriarty focuses on what they have in common. Sherlock focuses on the differences.

Even if Sherlock chose the other side, chose to share the angels side, he isn't one of them - and neither is Moriarty. But there is the difference between what you are and what you chose. It makes Sherlock a person John puts up with. John would argue that Sherlock was nothing like Moriarty. Because he can see that Sherlock makes different choices. But Moriarty can see that Sherlock could have been him, and is him, in a way - prepared to do anything. I think Sherlock is aware that Moriarty has a true point there.

On the rooftop, Moriarty isn't so keen on keeping their game going anymore as he was back at the pool. He could have called back the killers, could have continued with Sherlock... like he did at the pool scene. But he doesn't this time. He again chooses what to do - and this time he chose to die. Sherlock told John that Moriarty is in prison because he chose to be there - and dying is also Moriartys choice. Somehow the "you are me" gives him enough reassurance to die.

So I do think Moriarty was looking for an equal not an adversary. And I don't think he thanks Sherlock because Sherlock has proven he can beat him. But more because he isn't better in fact, I think Moriarty thanks Sherlock exactly for being "him", not being more but also not being less. Quite a compliment - or insult, depending on the view.

Remember that earlier in the scene Sherlock is holding Moriarty over the ledge and says, with some surprise--or at least dawning realization--"You're insane."  To which Moriarty replies, "You're just getting that now?!"  Now Sherlock is not a normal person and even calls himself a sociopath, so for Sherlock to call another person insane means waaaaay out of bounds.  

So who knows what exactly Moriarty sees in Sherlock, but it is not necessarily rational or even sensical.  Maybe Moriarty sees Sherlock as a fellow god, as another person who has transcended normality.  That would fit with the "Thank you" and "Bless you."  

Do not gaze long into the abyss....