WE PROPOSE A PROGRAM OF ARCHIVAL X-RAY AND RELATED STUDIES DESIGNED TO ADVANCE UNDERSTANDING OF THE REMARKABLE ACTIVE GALACTIC NUCLEUS (AGN) POPULATION OF X-RAY WEAK QUASARS. THESE EXCEPTIONAL OBJECTS REVEAL PHENOMENA THAT ARE MORE GENERALLY APPLICABLE BUT ARE DIFFICULT TO INVESTIGATE WHEN MORE SUBTLY EXPRESSED IN THE OVERALL QUASAR POPULATION. X-RAY WEAK QUASARS FURTHERMORE CHALLENGE A CENTRAL TENET OF X-RAY ASTRONOMY THAT LUMINOUS X-RAY EMISSION IS A UNIVERSAL PROPERTY OF EFFICIENTLY ACCRETING SUPERMASSIVE BLACK HOLES; THIS IDEA UNDERLIES THE UTILITY OF X-RAY SURVEYS FOR IDENTIFYING AGNS THROUGHOUT THE UNIVERSE. OUR PREVIOUS FINDINGS INDICATE THAT UNDERSTANDING OF X-RAY WEAK QUASARS IS NOW PRIMED FOR RAPID FURTHER ADVANCES.