SWMM 5 does not have a explicit timer in its Real Time Control (RTC) rules but you can approximate it by using a Control Curve as in the attached example model. The Control Curve will modify the setting of the Weir by the Inflow to the Storage node. You can have normal weir flow settings based on the invert elevation of the weir and the Surface node water surface elevation but in addition you can control the weir setting by:
1. Closing the weir when the inflow is low,
2. Closing the weir by staggered Storage node depth,
3. Opening the weir gradually when the inflow increases
4. Closing the weir by a combination of Node Depth IF statements and Control Curve rules
For example, you can have the Weir Setting controlled the Node Depth, Link Inflow and Node Inflow simultaneously approximately with the depth and the inflow parameters closing the weir by proxy instead of by time since the closing.