Hi,
In my experience, the only practical way to control duckweed is by netting. Fish and ducks are a non-starter with amphibians, as are herbicides. They also increase nutrient levels. Covering the pond basically involves starting again and again will cause deoxygenation and release of nutrients (much the same effect as the duckweed really).
That's the bad news. The good news is that it IS possible to get rid of duckweed by assiduous and frequent netting - but like any invasive plant, don't let quantities build up. And net the pond in autumn to intercept falling leaves.
A healthy community of pond plants will help to absorb the nutrients on which duckweeds thrive. In particular, rooted species such as pondweeds, milfoils and water lilies are good. Free-floating plants that are much easier to control include water-soldier (Stratiotes) and frogbit (Hydrocharis morsus-ranae). I have some spare if you need any (all UK native) - pm me if interested.
Tristan