In recent laboratory experiments, varying nucleation locations of accelerating slip with changing nucleation lengths were observed. Spatial variations in effective normal stress, due to the controlling influence on fault strength and fracture energy, play an important role. We quantitatively explain how spatially heterogeneous effective normal stresses affect earthquake nucleation and slip behavior. We simulate a meter-scale laboratory experiment in a numerical earthquake sequence model with stochastically variable normal stresses. We identify five regimes of earthquake nucleation and slip behaviors, controlled by the ratio of the heterogeneity wavelength (\(\lambda\)) to the nucleation length (\(L_c\)). When \(\lambda\) is much smaller than \(L_c\), full ruptures are observed. Slip rates and recurrence intervals are similar to those on homogeneous faults with comparable averaged normal stress. When \(\lambda\) is much larger than \(L_c\), slow slip events and partial ruptures occur frequently and the nucleation length of each earthquake depends on the local stress level. We find locations of nucleation and arrest in both low and high normal stress regions (LSR and HSR, respectively) when \(\lambda\) and \(L_c\) are of the same magnitude. When \(\lambda\) is larger than \(L_c\), earthquakes nucleate in LSRs, and arrest in HSRs. However, HSRs and LSRs switch these roles when \(\lambda\) is smaller than \(L_c\). Interestingly, we observe that nucleation migrates from an LSR to its neighboring HSR in one earthquake, when \(\lambda\) is between the minimum and maximum local nucleation lengths. We observe a large amount of aseismic slip and associated stress drop in the initial LSR, which might be linked to the migration of foreshocks as documented in natural and laboratory observations. This improved understanding of earthquake nucleation is important in estimating the seismic potential of different fault patches for natural and induced seismicity.