In this work we combine magnetization, pressure dependent electrical resistivity, heat capacity, Cu63 nuclear magnetic resonance (NMR), and x-ray resonant magnetic scattering experiments to investigate the physical properties of the intermetallic CeCuBi2 compound. Our single crystals show an antiferromagnetic ordering at TN≃16 K and the magnetic properties indicate that this compound is an Ising antiferromagnet. In particular, the low temperature magnetization data revealed a spin-flop transition at T=5 K when magnetic fields of about 5.5 T are applied along the c axis. Moreover, the x-ray magnetic diffraction data below TN revealed a commensurate antiferromagnetic structure with propagation wave vector (0012) with the Ce3+ moments oriented along the c axis. Furthermore, our heat capacity, pressure dependent resistivity, and temperature dependent Cu63 NMR data suggest that CeCuBi2 exhibits a weak heavy fermion behavior with strongly localized Ce3+ 4f electrons. We thus discuss a scenario in which both the anisotropic magnetic interactions between the Ce3+ ions and the tetragonal crystalline electric field effects are taking into account in CeCuBi2.