I always got the impression that the letters were coming from Farengar, the mage in Dragons Reach. Speaking with him gives me the impression that he may be an ex-blade and is trying to help you without getting directly involved to expose himself. I lean toward this hypothesis, because Delphine tells you she got her information about the dragon burials from the dragonstone that you had to give to Farengar. My guess is that he passed the stone on to Delphine after examining it.
Just my $0.02,
i was thinking the same thing