Summary: We report a combined experimental and theoretical study on intriguing magnetic properties of quasiferroelectric orthochromates. Large single crystals of the family of RECrO3 (RE = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds were successfully grown. Neutron Laue study indicates a good quality of the obtained single crystals. Applied magnetic field and temperature dependent magnetization measurements reveal their intrinsic magnetic properties, especially the antiferromagnetic (AFM) transition temperatures. Density functional theory studies of the electronic structures were carried out using the Perdew-Burke-Ernzerhof functional plus Hubbard U method. Crystallographic information and magnetism were theoretically optimized systematically. When RE3+ cations vary from Y3+ and Eu3+ to Lu3+ ions, the calculated t-e orbital hybridization degree and Néel temperature behave similarly to the experimentally determined AFM transition temperature with variation in cationic radius. We found that the t-e hybridization is anisotropic, causing a magnetic anisotropy of Cr3+ sublattices. This was evaluated with the nearest-neighbor J1-J2 model. Our research provides a picture of the electronic structures during the t-e hybridization process while changing RE ions and sheds light on the nature of the weak ferromagnetism coexisting with predominated antiferromagnetism. The available large RECrO3 single crystals build a platform for further studies of orthochromates.