Of the 8 figures with the short diagonal c2 elements alone colocated 1 is disconnected, leaving 7 novel tiles.
For 6 of the tiles when the weight function is plotted show a ribbon (in green) where only half the corresponding area of the plane is covered by the tile. The seventh tile has a discontinuous green fringe, rather than a ribbon running through the tile.
Two copies can (obviously) be put together to tile a symmetric tile. The images below show one copy in red, and a copy rotated 180° in blue; the overlapping areas (the ribbons) are shown in magenta.
© 2015 Stewart R. Hinsley