The occurrence of fluid-induced aseismic slip or slow slip events along faults has been reported in many studies, but their underlying physical mechanism and its impact on induced seismicity remain unclear. In this study, we develop a numerical model that incorporates fluid injection on a fault governed by rate-and-state friction to simulate the coupled processes of pore-pressure diffusion, aseismic slip, and dynamic rupture. We establish a field-scale model to emulate the source characteristics of induced seismicity near the Dallas-Fort Worth Airport (DFWA), Texas, where events with lower-stress drops have been observed. Our numerical calculations reveal that fluid pressure diffusion modifies fault criticality and induces aseismic slip with lower stress drop values (<1 MPa), which further influences the timing and source properties of subsequent seismic ruptures. We observe that the level of pore-pressure perturbation exhibits a positive correlation with aseismic-stress drops but a reversed trend with seismic-stress drops. Simulations encompassing diverse injection operations and fault frictional parameters generate a wide spectrum of slip modes, with the overall scaling relationship of moment with ruptured radius following an unusual trend that is similar to what is observed in the DFWA sequence. Based on the consistent scaling, we hypothesize that the lower-stress-drop events in the DFWA may imply less dynamic ruptures in the transition from aseismic to seismic slip, located in the middle of the broad slip spectrum, as illustrated in our simulations.