Typically, stiffness values measured with the Light Weight Deflectometer (LWD) correlate poorly with density. Fundamentally, soil density and stiffness are two very different physical properties.
Density is a static behavior depending on grain density, grain size distribution etc. Density is of a measure of volume.
Stiffness is similar to bearing capacity or deformation modulus and is a measure over a given area.
Further, to meaningfully compare measurement methods, one must ensure the compacted area is homogeneous. This means that at every measuring point, the conditions must be the same material properties, moisture, grain size, thickness of layers, materials etc.