We had a large pond. Probably 70' x 300'.. It took up our whole backyard. It was 4' deep tapered down to 12' deep. When we bought the house, the pond was stocked with 6 Grass Carp (sterile), probably 20 Catfish, some Perch, and a shitload of Bluegill. We never had any problem with duckweed, which it sounds like you have. After a few years of living here, and the fish being grain fed, and the cattails taking over, the wife decided that she wanted some Koi. We split the pond in half. We drained it down to where the fish were still safe in the deep end. I bought a skidsteer and removed all of the junkyard gravel (the huge stuff) from around the pond because of weeds always growing, and used it and some other dirt to build a walkway across the pond.
We refilled the pond. On one end we added the Koi, and the other had the gamefish. At first we had a couple of dozen Koi and some goldfish that the wife bought. Soon we had a few hundred. They grow fast. The Koi were getting to be in the 1'+ range in size, along with probably 1#-2# goldfish.
On the gamefish side, the Bluegills were easily 1# or more with a 10" girth. The Catfish we now 24" in size and 30#'s in weight. The Grass Carp were pushing 3" in size and upwards of 50+ lbs.
By now, the cattails, and water lilies were taking over, and in the summer we were having the green algae. Plus from one small Water Iris, that had just a little stock of Bamboo in it took over one whole side and end of the pond in the banks, and was coming up 5-10' in the yard.
People were stopping to fish because we gave one person access to it, then they came with a friend, then that friend told a friend who told someone else. We finally made the decision to get rid of the Koi and goldfish as they were mutilating the pond banks. they would actually come up partly on the bank to eat whatever was green. Then they started undermining the banks. So we drained down the one end and got rid of the Koi. Then we filled in that end of the pond. One year though, we had a major rain, and a couple of Koi and goldfish made it to the other side. Big problem. Now they have bred and there is now a few hundred in there. We drained the pond, got the nets out, and got rid of all of the fish. We decided to fill in the other end, and just have a nice small pond in the middle of the yard with a fountain. BTW.....Bluegills will come if there is water. The eggs will come in on Herons legs, duck legs, and so on. And we must have missed a few goldfish when we filled in the one end. So the wife and I set down, talked about it, and filled in the middle section of the pond. Now all we have is a large back yard.
That is one of the best things we ever did. The pond was nice and enjoyable at times, but it never was a natural pond. The guy that had the house built had the pond built. Everyone told him it would never hold water. So he kept it filled with a garden hose in periods of drought. Then we had people showing up when we were not at home, fishing. It was just a hole in the ground with water in it and one of the biggest pain in the asses there was.
So take it for what it is. We had the Sterile White Amur (grass carp), Bluegill, Catfish, Perch, Koi, Goldfish, Bullfrogs out the wazoo. We still got algae although we would treat it with Copper Sulphate, and we dyed the water blue to help eliminate it. But the Cattails took over all around the pond, we did have duckweed, although not covering the surface fully, the lilies were taking over, and the fish were out of control.
Pick your fish wisely!!!!! And pick your plants wisely also!!!!