Welcome!
My WAG is 1 3/4 acre. If the fish are fat and happy, then the pond sounds pretty balanced. There is a lot of vegetation due to the clear water (without a certain amount of light it won't take root and grow). The vegetation is feeding on the nutrients in the pond, which is a good thing if you want clear water. The vegetation is providing habitat for the smaller fish to hide in to escape predation, but by the description of the predators, it isn't excessive, although it's a PITA to fish thru.
Pick your poison; Ideally, with 18" to 24" of water clarity, plants won't grow in deeper water. To get that, you'll probably need something to jump start a photoplankton bloom. The downside? Bye,bye clear water.
It sounds like the pond is pretty well balanced. If you can take some close-up pictures of the weeds, someone here probably could identify them. You might be able to treat some of the weeds with a chemical to knock some of them back if you have too many. Don't knock too many of them back because you might have a fish kill due to lowering the ozygen levels in the pond with the decaying weeds.
If you look in the little box in the upper left corner of this page that says "Main Menu", click on Resource Guide, then click on "Fisheries Consulting Service". There should be someone there that would come out. I know for sure that Greg Grimes and Bob Lusk are frequent contributors here (Bob is one of the co-founders of this forum). I'd do that and make some phone calls or e-mails before doing anything on my own with such a great sounding pond (well, tank

).