In regards to the Gryffindor fireplace, why WOULD they be keeping watch on it? Sirius had defected to the Death Eaters (so they thought), so why would be be all that bothered about visiting his old common room?

And before anyone says "to get Harry", what would be the point of looking through the fireplace? All it would do is alert Harry to his proximity and make him easier to find. Sirius would have had nothing to gain through the fireplace access, therefore why watch it?