I have a 1/4 acre pond averaging about 8-10 feet deep in Northeast, TN. In 2020, we had the existing 1/8 acre pond mucked out to the average 8' depth, then enlarged it to double the size to about .25 acres.
Each year, we've had a major problem with duckweed covering the entire surface.
Currently (Jan '22) the pond water is opaque with clay sediment from the excavation but is steadily clearing.
The pond is spring fed, with one of the springs about 400' away run through a 2" pipe with a sediment trap. Flow from the main spring is about 14 gallons/minute. If my math is correct, the pond turns over every 145 days or so.

Questions:
Would aeration be beneficial considering the turnover rate?
How many diffusers should I use and at what depth?

Thanks.
Edit: Would it be beneficial in any way to wait until the pond clears on its own before installing the aerators. Based on the experience when we had it mucked out, that will take about another months.

Removing a significant amount of the nutrient laden muck should eliminate the duckweed problem. Going forward you might see a lot more filamentous string algae.
Bottom diffused aeration will definitely shorten the turnover rate to easily once a day. One dual head diffuser with air 2.5-4cfm from a 1/4hp air compressor (rotary or rocking piston). should be able to create a water turnover in 3 to 5 hours. Depending on shape of the pond you might be able to get adequate pond mixing by running the pump with 2 diffusers two hrs per day.

I suggest definitely wait until the pond clears up to 2.5 to 4 ft of visibility before running / installing an aerator. If you start the aerator with very fine silt still in suspension the aerator mixing will tend to keep the smallest silt particles in suspension. If the pond gets some ice cover this helps clear the water. Generally the water is clearest in a pond just after ice out due to the prior period of no wind action and very slow biological activity during cold water of winter.

My second pond suffered from clay suspension after every rain. When I installed aeration, it went to being cloudy all the time.

One FEL full of limestone screenings (which includes sizes from fines to about #57; we keep it in stock to mix with manure when spreading) caused the clay to settle out permanently. I add another FEL load every two-three years.

Adding limestone also increases ph buffering; I don't think it can hurt anything. A lime search here (or words from one of our water quality experts [Cough! Cough! Bill Cody] will let you know what forms of lime are safe to use in ponds.

Look in the January - February 2019 issue of Pond Boss magazine on page 20 for an article by Dr. Boyd for all one needs to know about lime, its forms and how to use it in ponds. AGRICULTURAL LIMESTONE TERMINOLOGY. Dr. Boyd tells all the details about limestone. Very Informative. He discusses, how limestone works, particle size (fineness index), solubility, effective neutralizing potential (ENP), neutralizing value (NV), and liming rates.

One think I'd do is consider sending a sample of the incoming spring water to be tested for nutrients if you don't know where the source of the water is. For instance, if the water source has a pasture above it that has a lot of livestock on it, it could be contributing to your nutrient loading and duckweed problem.

I agree with esshup about testing a sample.

You can even try a preliminary test with just a glass bottle. Put a sample of murky water in a dark closet for three days. If it is still murky, then you definitely have a chemistry problem! That problem requires a true sample test so you can have data to apply the correct response.

Thanks for the great info!
It's funny, but the progression of the algae/duckweed was the other way around. We had tons of the filamentous algae, but after we had the pond mucked out, the duckweed took over.
I will wait until the pond clears to add the aeration.
Most of the agricultural activity in the watershed is our own animals (Pigs, chickens, and goats.) I suspect that the nutrient levels are high and due to runoff from our pastures more than from the spring. I'd be curious to get both the pond water itself tested and the spring water to test my theories.
I did the settling test with a sample after the pond was mucked out but not after it was enlarged, so it's probably worth trying again. I also did a test with gypsum and chose not to use it because it didn't affect the settling/clearing rate much.
Among other things, we use our pond to irrigate our 1 acre blueberry field. Blueberries require an acidic pH, so adding lime to the water isn't an option for us. Gypsum would be an alternative, but might not have much benefit as per the test I did above.
Thanks again.

TN - normally duckweed thrives when more dissolved nutrients are present compared to filamentous algae. Mucking out a pond could release excessive nutrients accumulated in the muck layers. Another option is animal manure contributes lots of dissolved materials that favor the duckweed. When one wants to grow duckweed the nutrient stimulus and "most economical nutrient sources are wastewater effluents from homes, food processing plants, cattle feedlots, and intensive pig and poultry production. Solid materials, such as manure from livestock, night soil from villages, or food processing wastes, can also be mixed with water and added to a pond at suitable levels." I often see duckweed very abundant in roadside ditches that receive septic effluent which indicates the conditions that favor duckweed.
Regardless the nutrient balance after 'mucking out' resulted in excessive nutrients that favors duckweed. It is possible that after winter the nutrient balance shifts to again favor filamentous algae. A product like PhosLock used properly at the correct rate should bind excess dissolved phosphorus that should reduce all FA and duckweed growth. To get plant growth under better control in the pond nutrient source inputs should be restricted or minimized