THE BROAD C IV EMISSION LINES IN WEAK LINE QUASARS (WLQS) ARE SIGNIFICANTLY WEAKER THAN EXPECTED FROM THE ANTI-CORRELATION BETWEEN C IV EQUIVALENT WIDTH AND THE HB-BASED EDDINGTON RATIO. THIS DISCREPANCY MAY BE RECONCILED IF THE EDDINGTON RATIOS OF WLQS ARE HIGHER THAN THOSE INDICATED BY HB. WE AIM TO TEST THIS HYPOTHESIS BY MEASURING THE HARD-X-RAY PHOTON INDEX IN ALL WLQS WITH HB MEASUREMENTS THUS OBTAINING ROBUST DETERMINATIONS OF THEIR ACCRETION RATES. STEEP SPECTRAL SLOPES WILL INDICATE THAT HIGH ACCRETION RATES ARE RESPONSIBLE FOR THE LINE WEAKNESS IN WLQS. OTHERWISE, ADDITIONAL PARAMETERS MAY CONTROL BROAD EMISSION LINE EQUIVALENT WIDTHS. THE RESULTS WILL YIELD CRUCIAL INSIGHTS ABOUT THE ACCRETION PROCESS AND BROAD EMISSION LINE FORMATION IN ALL ACTIVE GALACTIC NUCLEI (AGN).