Post Process Materials cannot be controlled gradually with the Blend Weight the Material has.
Instead it works as a On/Off switch. (0 means off, everything else means on).
I would suggest to route this particular BlendWeight to the Post Process Material itself.
We already have something similar for Post Process Materials.
for example is available in HLSL Code when using Pre-Tonemapper Post Process Materials.
Having an additional Blend Weight Parameter thats just “always there” would make things a lot easier since the Smooth Blend Weight when getting in/out of a Post Process Volume is not possible to get and route to a Material.