In The Hound of the Baskervilles, why does Watson’s heart leap when he reads a note in the stone hut?Note says: “Dr. Watson has gone to...

This happens at the end of Chapter 11.  To be precise,
Watson's heart does not leap when he reads the note. 
Instead, his heart leaps when he sees that there is a note,
even before he has read it.  We can see this from the following
quote:

As I
set it down again, after having examined it, my heart leaped to see that beneath it
there lay a sheet of paper with writing upon it. I raised it, and this was what I
read...

As you can see, his
heart has leapt before he has seen the content of the
note.

His heart leaps at that point because he is in the
hut searching for clues.  When he sees a piece of paper with writing on it, he naturally
becomes excited because he thinks that he has discovered a clue that might tell him who
the man in the hut is and why he has been living
there.

Later, after he has read the note, Watson is excited
for another reason.  He now believes that he is the one who is being stalked.  This of
course excites him and makes him apprehensive.