Why did Yoda and Palpatine talk about Anakin?

Question

At the beginning of Duel in the Senate Yoda enters Chancellor's office and says:

• I hear a new apprentice you have, Emperor. Or, should I call you Darth Sidious?

Later, they exchange these words:

• You will not stop me. Darth Vader will become more powerful than either of us.

• Faith in your new apprentice, misplaced may be, as is your faith in the dark side of the Force.

All this sounds a bit weird, looks like they are fighting over Anakin (who would control him), not because eternal enmity between Jedi and Sith. Remember, Palpatine just orchestrated killing of so many Jedi, Anakin killed younglings, yet Yoda doesn't mention anything of that. He sounds almost like Palpatine stole his new shiny toy, and he wants it back. On the other hand, Palpatine admits that Anakin would become more powerful then he is. Yet, he doesn't seem to be upset about that, he sounds glad - very strange for a Sith.

Answer 1

Anakin has the most force potential of any force user in the galaxy, and is believed by the Jedi to be the prophesied chosen one who will bring balance to the force (first mentioned in episode 1). As such, he would be seen as pretty important to the Jedi's fight with the Sith.

The first quote is probably just Yoda making Sidious aware that he knows Anakin has betrayed the Jedi, and that Sidious is a Sith. Basically that he knows what is going on. Nothing terribly unusual here.

From Sidious' perspective, recruiting him is a major coup and worth gloating about. Certainly, Sidious is commenting on his potential here. Given the Sith have the whole rule of two going on where in theory each apprentice will ultimately succeed their master and prove themselves the stronger, the expectation that Anakin/Vader will become stronger than Sidious is not so strange.

Finally, the last quote suggests that Yoda still places some hope in the prophecy, and that Anakin may still bring balance by destroying Sidious. At this point, most of the audience should have seen Return of the Jedi, so we know this actually happens. Out of universe, it is most likely intended to foreshadow this.

It is also worth noting that George Lucas has stated that he views Star Wars as being to story of Anakin. While it is possible that this wasn't always the case (he seems to have had a habit of changing his mind), it is now his publicly stated opinion. This is likely to have influenced his focus here around Anakin.