I thought I read on here that duckweed is prolific in ponds that have a lot of organic nutrients in it, and poor aeration.
If I was draining it, I would get the muck out of there at the same time. No way to tell how much muck there is in there. Well, actually there is. I think Esshup has described a way to do it.
Then since it is near your house, run aeration to it. You could wait on this and do after it fills up again.
