Are you using a plate/wing combo or a bcd with a 2" waist belt (like a SP LiteHawk, AL Outlaw, etc.)?I have considered moving to an integrated BCD, but my wife dives one and it has no room in the pockets for accessories like slate, cutting tools, sausage, etc.
My weight belt is one with pockets that allows me to place the weight up close to the buckle.
With the configuration I have now with trims on the tank strap, I can maintain a good posture in the water column comfortably.
If so there are a number of pockets that would give you both weight pockets and stowage pockets, either combined or separate.