Weepwood Logs and Mossy Weepwood Logs can be found on green Grass or in Bog Water, but only in Swamplands close to Weepwood-trees.
Weepwood Logs can alternatively be created by using an equipped Plow on blocks of common Weepwood.
Mossy Weepwood Logs cannot be harvested as such, but will instead turn into common Weepwood Logs, sometimes with additional units of Moss.
Weepwood Logs can be chopped into Wood Slabs and/or Wood Rods in a Processor.
Weepwood Logs can also be used for crafting recipes that will accept any kind of Wood (except for Corrupted Wood) or Log except for Ashenwood Log.
Most Logs can be used as Fuel for Forges; 2 blocks of Weepwood Logs will be needed for each process (of melting or hardening), and they will burn rather slowly. Weepwood Logs cannot be corrupted currently (as of R39 in February 2017), however Corrupted Wood makes a much more powerful Fuel.
Most Logs are flammable, so be careful when putting torches onto or especially under blocks of Logs (or any other block of Wood or Leaves) in hot environments like Savannas, Shores or Jungles. Fire is able to spread onto other flammable materials and such a wooden house or whole forest can burn down.
You cannot extinguish such a fire by using Water or other liquids, but only by creating aisles wide enough so flames won't be able to leap over or by claiming the area and disabling the option for fire spread. Players who bought the "Pro" upgrade can also disable the fire spread option for their whole gameworld.