There is no answer to duckweed im afraid. I had it in my goldfish pond and i ended up stripping the lot out, buying a new liner and putting new plants and fish in from a duckweed free scource.
Scooping it out daily will do the trick but you end up getting paranoid that you've left a bit in there....and you usually have.
There's reports that grass carp might eat it but again, not reliable enough and UV's wont touch it..
Strangely enough, i had it in my tropical tank and my Congo tetras devoured it within 2 days....Tinfoil barbs apparently do the same. maybe you could borrow a few large Tinfoils during the warm weather then return them !!!!!!!