What kind of Aldrovanda is it? Temperate (turion-forming in winter dormancy) or tropical (evergreen)? They may require different temperatures...?
I grow the temprate type (from Poland) very sucessfully. I keep it very well lit with a degree of direct sun for a few hours a day (from around 9am to 2pm in summer). I wouldn't think duckweed would be anything other than a bloomin' nuisance in an Aldrovanda tank. I posted recently about it on CPUK, but I will repost here:
It shares the container with
Utricularia stygia. My method is almost the same as for other aquatic utrics except the depth of water and the substrate.
It's in a household, opaque, plastic storage box, 18" long, 12" wide and 8" deep. On the base is 2" of peat overlaid with a thin layer of sharp sand. Then on top of this is a 2" layer of sedge litter, which was boiled in two changes of water before use. The water depth is therefore clear for only 4". The water is rainwater in which peat was boiled and then strained out.
The plant gets bright light and air temps up to 32C. Planted in the same container in 5" square mesh pots standing on the peat are typha minima and carex panicea, and a small water hyacinth floats on the top. A number of small water snails graze in the tub, and it gets a bag of fresh daphnia every month or so (the Aldrovanda and utric gobble most of them up quickly!) to assist against algae. Once the tank is stabilised against algae (which occurs as the utrics and aldrovanda start out-competing it), then it ceases to be a problem.
Here is some pics of mine a few days ago, in soul-elevating flower - yay!!
Best wishes.
Rob.