I think it's best to make your peace with duckweed and leave it alone. It might look like scum from a distance but it's actually very clean.

From Wikipedia:

Duckweed is an important high-protein food source for waterfowl and also is eaten by humans in some parts of Southeast Asia. As it contains more protein than soybeans, it is sometimes cited as a significant potential food source.[6] The tiny plants provide cover for fry of many aquatic species. The plants are used as shelter by pond water species such as bullfrogs and bluegills. They also provide shade and, although frequently confused with them, can reduce certain light-generated growths of photoautotrophic algae.

The plants can provide nitrate removal, if cropped, and the duckweeds are important in the process of bioremediation because they grow rapidly, absorbing excess mineral nutrients, particularly nitrogen and phosphates. For these reasons they are touted as water purifiers of untapped value.[7]

The Swiss Department of Water and Sanitation in Developing Countries, SANDEC, associated with the Swiss Federal Institute for Environmental Science and Technology, asserts that as well as the food and agricultural values, duckweed also may be used for waste water treatment to capture toxins and for odor control, and, that if a mat of duckweed is maintained during harvesting for removal of the toxins captured thereby, it prevents the development of algae and controls the breeding of mosquitoes.[8] The same publication provides an extensive list of references for many duckweed-related topics.

These plants also may play a role in conservation of water because a cover of duckweed will reduce evaporation of water when compared to the rate of a similar size water body with a clear surface.

You might try to stop the runoff of fertilizer into your pond.