Maybe you can get something that eats the Duckweed? Like a duck. A quick google also revealed that Grass Carp & Koi will eat duckweed. I don't know much about ponds in general or your pond, so I don't know if any of those solutions will work.

Here in Asheville we have such a creative community that you can actually rent a goat to eat weeds and poison ivy. I don't know if you can rent a duck to eat your duckweed.

I don't think the pond is big enough to support grass carp or ducks, but I have heard similar solutions.

Don't think anyone rents ducks locally, but like your local solution to weed control :)