I'm going to take a different tack on this question. The OP asks:

Lots of people die in the story. Most of the time, we don't expect them to come back. Characters themselves don't expect other characters to come back.

There is a big difference between the character of interest here, and other characters who have died. Mainly: In the books, this character is recently dead, there are many unknowns about him, and many theories about him (see answers by Skooba and Dima for one such, more can be found here).

With other characters - such as Ned Stark - it was known that these characters were going to die. And even after it became known that death was not as permanent as it once seemed, it seems clear that these characters were not coming back. With the character of interest here, these things are no longer givens. We know that:

1. The death is recent enough that coming back is a possibility.
2. There is someone in the vicinity who can bring people back.
3. There is speculation that this character is not all that meets the eye.
4. The books have not progressed the story far enough to know the answer.

These four things, taken together, generate the elevated interest regarding this particular character's status compared to others.

I'm going to take a different tack on this question. The OP asks:

Lots of people die in the story. Most of the time, we don't expect them to come back. Characters themselves don't expect other characters to come back.

There is a big difference between the character of interest here, and other characters who have died. Mainly: In the books, this character is recently dead, there are many unknowns about him, and many theories about him (see answers by Skooba and Dima for one such, more can be found here).

With other characters - such as Ned Stark - it was known that these characters were going to die. And even after it became known that death was not as permanent as it once seemed, it seems clear that these characters were not coming back. With the character of interest here, these things are no longer givens. We know that:

1. The death is recent enough that coming back is not out of the question.
2. There is someone in the vicinity who can be reasonably supposed to be able to bring people back.
3. There is speculation that this character is not all that meets the eye.
4. The books have not progressed the story far enough to know the answer.

These four things, taken together, generate the elevated interest regarding this particular character's status compared to others.