I have 2 overflow weirs and one has 2x15mm bulkheads (one unrestricted and one backup) and the other has one 25mm bulkhead.
To quiet the single bulkhead weir I have to close the ball valve as Layton described. It completely silences the system because it raises the water level in the weir to the point where no vortex forms to suck air into. However, it also raises the water level in the tank to beyond where I like it. Also, if the return pump shuts off and then back on, as in a power outage, it takes the weir too long to equalize and the main tank overflows until the weir catches up and equalizes. So, I have placed the internal sponge from a return pump (I place the hole in the sponge directly over the hole in the bulkhead) over the bulkhead and it slows/diffuses the flow just enough to reduce the sound to a low gurgle without slowing it enough to overflow the tank in a restart.
The double-bulkhead weir is perfect because I have one working full stop and one as a backup and the water level in the weir is enough to eliminate any air being sucked into the bulkhead but if the water level gets high enough to overflow the tank, the backup bulkhead kicks in and compensates.
I have been thinking seriously about drilling another bulkhead in the 25mm weir.
So, both lduncan and suphew are right. However, in my system, lduncan's solution, while completely silent, means a wet carpet in a power outage. It remains to be seen whether drilling another bulkhead in the 25mm weir will have the same effect as in the 15mm weir due to the size of the bulkhead. To be silent, there has to be a fine balance between the amount of water that gets drawn through the weir and the amount of water that the bulkhead allows through with the depth of the weir and the water level in the tank as variables in the equation.
I hope this helps. I have been working through this same issue since I built the weirs almost 2 years ago.