Why did the Nazgul not succeed in Bree and on Weathertop?

[Raynor]

I've also had the impression that the Nazgul became more powerful the closer they came to Sauron in Mordor. During the passage of the Dead Marshes Sam and Frodo were more terrified by the cries of the Nazgul than they had been in the Shire.

According to the Tale of Years, RotK, that event happens ~two weeks before the attack on Minas Tirith. Concerning the witch-king at that time, Tolkien stated:

Originally Posted by Letter #210

The Witch-king, their leader, is more powerful in all ways than the others; but he must not yet be raised to the stature of Vol. III. There, put in command by Sauron, he is given an added demonic force.