Motivated by the presence of competing magnetic interactions in the heavy fermion family CeTX2 (T = transitionmetal, X=pnictogen), here we study the novel parent compound CeCd0.7Sb2 by combining magnetization, electrical resistivity, and heat-capacity measurements. Contrary to the antiferromagnetic (AFM) ground state observed in most members of this family, the magnetic properties of our CeCd0.7Sb2 single crystals revealed a ferromagnetic ordering at Tc=3K with an unusual soft behavior. By using a mean field model including anisotropic nearest-neighbor interactions and the tetragonal crystalline electric field (CEF) Hamiltonian, a systematic analysis of our macroscopic data was obtained. Our fits allowed us to extract a simple but very distinct CEF scheme, as compared to the AFM counterparts. As in the previously studied ferromagnet CeAgSb2, a pure |±1/2) ground state is realized, hinting at a general trend within the ferromagnetic members. More generally, we propose a scenario for the understanding of the magnetism in this family of compounds based on the subtle changes of dimensionality in the crystal structure.