GH Helix NIJ 06 is the lightest, thinnest, most comfortable vest I know of. The level II and IIIA are both available. I wear one myself.
For the officer that demands extreme comfort, the GH HeliX was designed to offer exceptional wearability by delivering a lightweight and flexible solution while meeting the rigorous NIJ Standard-0101.06. A hybrid construction of Spectra Shield® and Goldshield® materials, the flexibility of the package is apparent from the first touch. The GH HeliX is the first and last choice when the requirement for comfort is absolute.