With an overflow box this style (inside and outside box), it's essentially a siphon. As water drains from the outside box, the level in it lowers, sucking water from the inside box, in an attempt to make both the same level. Therefore, if you want to make water in the inside box higher, you must make it higher in the outside box. You may be able to do that with a standpipe or something in the outside box.
Sometimes, people tend to run so much flow through a small overflow, that the water becomes pretty noisy. Think about how a bubble trap in a sump works. If you run the right water flow, there are no bubbles created as water runs down the wall. If you run too much flow, it bubbles as it hits the water surface. You don't want your weir to have so much flow that you get noise or bubbles, for the same reason. Not only that, but any microbubbles will wind up collecting inside your siphon tube.
Something else I have done is gotten foam and put it in the inside box, so that the water would run down the inside of the box and hits it...stopping any bubbling and silencing noise. Just make sure it's in there tight or in a location that it can't stop up the siphon tube.