The older pond probably has a nutrient problem because of fallen leaves in the autumn; trees that are not our property have grown up to overhang the pond. We recently revamped the pond and restocked it with plants after a a major dredging, so hopefully things will balance out in time. The new pond is just a normal hole dug in the garden with a butyl liner. We don't use fertilisers in our garden. The duckweed hasn't got a hold yet, so hopefully all the other plants (Elodea, Nymphaea, Potomogeton, water forget-me-not) will outcompete it. I am also removing the little bits that I see.
The duckweed is a problem because it smothers the submerged plants byt blocking out almost all the light. The submerged plants then die, rot and cause the pond ecosystem to collapse, whilst providing more nutrients for the duckweed to grow. I don't mind having a little bit, as it provides cover for amphibians and invertebrates, but I don't want it to smother the pond by becoming too prevalent.
Thanks for the pointers.