Why Did the Nazgul Wait at Crickhollow?

[The Might]

You raise a very good question there littlemanpoet, why didn't the Nazgul follow him...this puzzles me indeed

I mean, even if they perhaps waited a bit to really make him feel fear it makes no sense to let him run away, especially if they suspected that he might have the Ring.
But as the Nazgul themselves say:

Let the little people blow! Sauron would deal with them later.

They probably expected someone to run and raise the alarm, what they did not expect is that the house was going to be empty.

But this raises another question, if they didn't follow Fatty because they noticed he doesn't have the Ring, why did they attack the house in the first place?
Were they really so overconfident that they were blinded by this and unable to notice the Ring was no longer in the Shire?

We see them usually as very capable and useful servants, but here they clearly failed...