I'm confused by your terminology. A weir is a straight fence with no notches/teeth. That is what it is referred to as in terms of flow dynamics. One of our mechanical engineers has a Flow Dynamics book and that's where I got my equation for calculating the necessary dimensions for a true C2C weir for a given flow rate and water height over the weir.
A notched weir is different, same calc but you have to throw in a constant to take care of the flow restriction created by passing the water through notches. Essentially you add up the width of all the notches and then multiply by 0.55. So if you have a notched overflow with 1/4" notches every 1/2" (so 1/4" teeth, 1/4" notch, etc) and that overflow is 48" long, that's 24" of total width but only 13" effective.
So if you have, say, 1/2" of water above the bottom of the notch in the 48" notched overflow, you would get the same flow rate across a weir that is only 13" wide.
If you make a really long weir, you can push a ton of water across it via a very thin profile (small water height over the top of the weir)
I think most people forget this and think if I have 1" of water on my notched box it's going to be maybe 1/2 that on a flat weir, because I'm just removing the notches. It's more like 4x less.