Lead sulfide quantum dots (QDs) have been widely used for various optoelectronic devices due to their high absorption coefficient and tunable bandgap. However, the low mobility of QD films results in poor charge collection and device performance. By combining QDs with graphene into hybrid graphene/QD photodetectors, photocarriers from QDs are transferred to graphene, improving charge collection and transport, drastically increasing the photoresponsivity. Herein, we carry a systematic analysis on how critical tuning parameters such as QD size and QD film thickness affect responsivity, spectral response, and time response. We report the absorption coefficient, refractive index (n, k), penetration depth, and energy bandgap of PbS QDs of different sizes. We study systematically how the photocurrent, photoresponsivity, time response, and power density dependence vary with QD size in hybrid Gr/QD. The bandgap of lead sulfide quantum dots was size-tuned between 0.86 and 1.39 eV. The time response shows that subsecond modulation can be achieved for different QD sizes with a responsivity up to 107 A/W at power densities of 10-5 mW/cm2. We also studied how the performance of the photodetectors is affected by the thickness, discussing the limitations on the thickness by the compromise between light absorption and charge collection. We describe how the optical response shifts toward the infrared as QD films get thicker. Time responses below 1 s are obtained for graphene/QD devices with thickness from 150 nm to 1 μm. This systematic study provides important guidelines to design hybrid graphene/QD photodetectors and tune their spectral response and performance.