The gas tank has nothing to do with it. If it's gray or blue smoke, it's oil. If it's white it's normal short term. If long term white, water into chamber. If it's black= fuel problem= Carb adjust, stuck float, sinking float, needle valve/seat, bad rebuild, airflow blocked by choke or air filter, vacuum leak. All those colors will cause rough running. Wet plug indicates plugs not firing, spark not strong or flooding from carb. Your gas tank is not wetting the plugs, the carb is. Clogged filters or gas line or tank block don't cause flooding. Except extra dirt can cause needle valve to stay open.
Better hope it's not a valve train problem. Timing or worse. BUT, there are a whole bunch of questions that need answered. Previous questions and we don't know if "rough" is during idle? no acceleration power? Runs good at speed? Hard start? stalls when driving? Color, duration and quantity of smoke?, etc. Focusing on the wet plugs is not where the focus should be. Can't believe two week old plugs have heavy carbon. An old motor will have some oil burning and if you take plugs out quick they could still have gas on some plugs. A motor still sucks gas in while coasting with no spark. The question is are they still firing good? After plugs get a good clean, does motor run for two weeks again? and etc. Testing and providing info here will save you a lot of money. It seems like you now want to find it yourself. That's OK. Good luck.
