hi E Little,
excessive duckweed is a sign of high "nutrients" in the pond
this may be from the fish or maybe from runoff from fields
if the pond is built from a ravine, there may not be
enough shoreline vegetation to remove nutrients and balance the system
so the pond may act more like a tank than a pond and may need flushed occasionally if possible
removing of duckweed will help get rid of nutrients (spread them on the garden and flower beds as mulch)
perhaps a floating island of plants could be used to remove the nutrients
but you should check for sources of nutrients
poisoning the duckweed may just cause an algae problem as the nutrients remain in the pond