Weepwood Logs can be used as Fuel for Forges; 2 blocks are required for each forging process, but they will burn rather slowly, since they are fuel level 1. Logs cannot be corrupted into better fuel types.
Logs are flammable, so be careful when putting torches onto or under blocks of Logs (or any other block of Wood or Leaves), especially in hot environments like Savannahs or Jungles, but also in Swamplands.
Fire is able to spread onto other flammable materials and such a whole Swamp forest and/or wooden house can burn down in the worst case. You can prevent this by claiming the area and making sure that the claim option "fire sim/spreading" is disabled (by default), or as a world owner you can disable this option for the whole game world.