I like all of the non-herbicide solutions first, but sometimes you can achieve better living through chemistry.
Purdue put out a good article on control of duckweed:
Control of Duckweed and WatermealOne of their non-herbicide recommendations is to reduce nutrients to the afflicted pond. Do you use any organic fertilizers on your blueberries that might wash into the pond? If so, then diverting this nutrient-rich surface flow away from the pond could reduce your duckweed problem.
They also make herbicide recommendations. There is a good "contact" herbicide (diquat) and a good "systemic" herbicide (fluridone).
I would recommend trying the diquat first and seeing how much control you can achieve. The treated pond is then safe for irrigation after 5 days.
The systemic treatment fluridone would probably give you better, longer-lasting treatment. (Sometimes the duckweed control may carry over to the next year.) However, the treated water cannot be used on irrigated edible crops for 30 days. It also cannot be used within 1/4 mile of drinking water intake pipes.
Hopefully, you can beat back the duckweed and FA with tilapia and other means. But you can probably use the diquat for assistance if your blueberries can take a week off without irrigation.
Good luck on your project!