No long term experience with duck weed as I've only had it twice, but both times it disappeared within 2 weeks after I stocked my Tilapia. I assumed they ate it since no other changes to my water were made.
Al is right on - duckweed is a minor problem when tilapia used as management tool as well as forage.
Small retention pond completely covered with DW - gone in two weeks after stocking tilapia - stopped spread into main pond as well - I have photos...