Crying Obsidian[1] refers to an abandoned project by Jeb[2] to implement a change-spawn obelisk[3].
Jeb has said[4] that this texture will be replaced by the grass-side texture in the 1.5 update, so this texture will not be used. Currently, it can only be found in the form of a texture in "terrain.png". This texture was added in Beta 1.3 but is currently not used in the game. It closely resembles obsidian, mostly due to the matching colors. It also appears to be a sandstone texture modified to look like obsidian. It is also known as "Bleeding Obsidian", "Mystery Block" and "The Meteorite" among many members for its appearance.
As of 1.5 the texture slot for weeping obsidian was replaced by a grayscale replacement of the side of grassy dirt blocks.