The weed thrives in shade and the crevices of a pathway. It thrives with moisture but is heat/drought tolerant and propagates vegetatively with a flat and dense matting effect as shown. Fine roots are 2 mm in length. Spread/growth is aggressive.
This is Common Liverwort (Marchantia polymorpha) a widespread weed, occurring from tropical to arctic regions. It commonly grows in container nursery stock; it can infest greenhouses and also grows in excessively moist areas in lawns and landscapes. Wikipedia gives you more information about this plant.
http://en.wikipedia.org/wiki/Marchantia_polymorpha
Controlling liverworts can be challenging. The most effective control is spraying them with landscape-grade acetic acid — this is simply vinegar, but an industrial-strength version. You can also manually pull them out. Fertilizing will actually help the liverworts thrive, so cut back on the fertilizer. Moist and damp conditions are ideal for liverworts, so reducing the amount of watering you do will also help.