Hey Kbuck, We had a severe Hydrilla problem, after several years of trying misc. methods etc, and, I also stocked 10 Grass Carp in our 9/10 of an acre pond who was eating the grass like crazy, and boy did those carp get big fast, however they couldn't put a dent in it.
I finally had to buy the dreaded (because of cost) herbicide. I bought a product called WHITECAP, it worked 10 times better than I ever thought, in fact I think my carp are going to starve now??
Here's a link http://lakework.com/site/
Call this guy(Greg Grimes) or drop him an e-mail, he is on this site a lot at the fishing forum also. He prescribed me an application based on the fact that I knew for sure what weeds I had. I later purchased the Whitecap thru another dealer and the product actually came from Greg. I didn't know he carried it, as I would have ordered from him first.
We had duckweed many years ago and used a Diquat product to eliminate it. The White cap says good for Duckweed, but we used it for Hydrilla and it worked excellent!
The only way to get rid of duckweed is to buy Sonar. It's about $700 a quart. 1 quart treats 1 acre. There are other chemicals that claim to kill duckweed but i've never seen them work. But first I would be certain that its duckweed.