It sounds like the pond is pretty much dead. What I mean by dead is that the oxygen levels in the pond are probably below that which would sustain fish life, less than 2 mg/l. You have your work cut out for you but if you are willing to put in some time and money you can get the pond in pretty good shape within a year or two. You probably do not have to drain it and dredge it out, contrary to what a lot of so called experts will tell you. Check the depth. If the pond has a minimum depth of 5-6 feet on average you will need to install aeration. Use a diffuser system with airstones on the bottom, not a fountain. Place the diffusers in the deepest area in the pond. If the pond is 2 acres you will probably need at least 2 diffusers. For a one acre pond use a 1/3 hp compressor with one diffuser assembly, for a 2 acre pond use 2 or three with a larger compressor, as much as 3/4 hp. Also, the shallower the pond the more diffusers you should use. If the pond is only on average 3-4 feet you will need more diffusers but if it has deep holes 8-10 feet you are okay with the minimum. Let me know if you need more specifics. Once you get it aerating the pond will begin to recover immediately. Oxygen will short-ciruit the nutrient supply to the duckweed and begin to starve it. But to speed up the process you might want to try to skim some off. By harvesting, you take nutrients out that are bound up in the plant. So this speeds recovery by tanking nutrients out in the form of the plant. Think of it this way. Duckweed is growing hydroponically on the surface because the nutrients are pumping from the bottom all the way to the surface. The aeration will stop the pumping but the plant will continue to grow for some time. If you remove some of what is there it will speed up the die off. I have done this personally on several ponds and it works in theory and practice. I cleared up one pond that was 1/2 and acre in less than 2 months. Another alternative is to use Sonar, Avast, or Reward herbicides to kill it, but the nutrients just go back to the water delaying recovery. Harvesting removes the problem nutrients once and for all. Harvesting is more of a restoration action whereas herbicides or sort of a band-aid approach and will probably have to be reapplied in the near future. As for the banks, you probably will need to just clear it up but don't go crazy. See what is there and what you can tolerate and cut out the rest. The bank vegetation dumps leaves each year that cause problems for the pond by creating a pool of nutrients and organic material. This is what causes the muck on the bottom. The aeration will also take care of this. Oxygen will begin to decompose the bottom muck. It is hard to say more based on what you have posted but I am quite certain that what you have is restorable given a little bit of effort and tender loving care.