Hello,
I am not sure that what you do is correct. A very shallow weir in the exit could give a transcritical flow, then the condition on depth should be relaxed otherwise you could see strange effects, like velocities entering because the prescribed elevation at the exit creates a step... Anyway I would start first to establish a steady state with a constant free surface elevation at the exit. For example if you start with constant elevation in your domain, and a slightly lower elevation at the exit, the flow will clearly go out. Then if it works you can start applying the stage discharge curve, with relaxation so that it evolves smoothly.
Regards,
Jean-Michel Hervouet