I have three ponds also. The front one and the back one are covered
in duckweed, but the middle pond (near the house) doesn't have a bit.
I know it has been "inoculated," I've seen ducks, cormorants, ibises,
egrets, and others visit the pond. I've even seen duckweed floating
in the pond, but I guess it just dies out because the pond stays free
of it.

I've been a cave explorer for some 40+ years and now live in some of
the best cave diving country in the world (northern Florida). Having
spent so much time underground and having friends that actually swim
around in the underground water I am extremely anal about putting any
kind of chemical where it can get in the ground or groundwater.
Herbicides are right out for me. I have no fish in the pond, either.
I haven't the foggiest why I don't have any duckweed there.

I've tried to search for solutions but haven't found hardly anything
promising. Methods of biological control (mainly fish that eat
duckweed) have mixed reviews, the majority seem to think it a pretty
iffy proposition, if not an outright poor method of control.
Mechanical methods (skimming and the like) seem to provide only very
temporary fixes. That leaves chemical methods (herbicides), and aside
from my reluctance to go that route it isn't a cheap way to go,
either. Besides, just about anything that kills duckweed kills a lot
of other stuff too, there doesn't seem to be anything like a duckweed
specific herbicide.