Here in south Louisiana, duckweed is normal. Everyone has it because of all the wading birds.
From what I have learned, 1 domestic duck per acre is a good control. Of course wild ducks fly in, and we have no control over that.
Duckweed is not widely hated around here. It produces lots of oxygen, and I understand some of it gets into the water. It can shade out deeper weeds that are hard to control. In the right amounts duckweed takes up excessive nutrients and prevents excessive algae bloom.
I don't know if it's coincidental or not, but ever pond and lake I have seen with duckweed in moderate amounts has very pretty water and healthy fish populations. I'm not trying to sell you on duckweed. It does need controlling or it will dominate. When I finish my new pond, I am going to get 1.5 ducks, no doubt.