Triangular lattice (TL) materials are a rich playground for investigating exotic quantum spin states and related applications in quantum computing and quantum information. Millimeter-level single crystals of REBO3 (RE = Tb-Yb) with a nearly perfect RE-based TL have been successfully grown via a high-temperature flux method and structurally characterized via single-crystal X-ray diffraction. These 113-type materials crystallize in a monoclinic crystal system with a C2/c space group. Anisotropic magnetism and dominant antiferromagnetic interactions are found for the above materials based on DC magnetic susceptibility measurements. The comprehensive low-temperature specific heat data of REBO3 (RE = Tb-Tm) are characterized on single crystals for the first time, which exhibit diverse magnetic behaviors. Specifically, two weak-field-induced transitions could be found in the case of DyBO3 based on the specific heat measurements. Our results suggest that REBO3 (RE = Tb-Yb) is a TL magnetic system for investigating potential quantum magnetism.