Hello everyone. I have an update to this thread. Sorry I got busy with other work and only recently came back to this project.
First of all, I realized the nodes I was selecting for the upstream and downstream boundary of the weir were not entirely accurate.
I have drawn the weir boundary (represented as a rectangular hole in the mesh using a shapefile polygon as hardline in blue kenue). In this figure I have drawn the nodes at the upstream and downstream weir boundary. The nodes marked by the arrows (nodes at the 4 corners) should NOT be included in the weir definition file. Including these 4 nodes resulted in unstable simulation with kilometers of water depth lol.