In case of suppressed weir, the flow width is equal to the total width hence confined air space is created below nappe because from top we have sheet of water, from sides we have channel walls and from bottom we have the channel bed. This confined space needs to be aerated as otherwise (-)ve pressure would be created in it and nappe will be sucked in leading to greater discharge for the same head. 
Thus, calibarated discharge formula Q = KH^3/2 will not hold good at all times since suction at different time will be different. 
Thus, to ensure that the same relationship between Q and H holds at all times, the condition at all times should be same and this is possible when confined space is ventilated.