Duckweed performs photosynthesis. Photosynthesis produces oxygen. They take in carbon dioxide and produce oxygen. So, when it is kept in the light cycle it will produce oxygen which will get dissolved in the water.
But the flask with water does not contain dissolved oxygen. So, at the end of light cycle the flask containing the plant will have more DO.
Now, in dark the plant does not produce oxygen. Instead it uses it to break the glucose and produce carbon dioxide. While this is not the case with the flask without the weed.
So, the flask without the plant will have more DO then the flask with the plant.
So, at the end of light cycle the flask with the weed will have more oxygen while at the end of dark cycle the flask with water will have more DO.