Two dinuclear cobalt(ii) complexes, [(dmso)CoIIL1(μ-(m-NO2)C6H4COO)CoII(NCS)] (1) and [(dmso)CoIIL2(μ-(m-NO2)C6H4COO)CoII(NCS)] (2) [dmso = dimethylsulfoxide, H2L1 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-methoxyphenol) and H2L2 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-ethoxyphenol)] have been synthesized and structurally characterized by single-crystal X-ray diffraction, magnetic-susceptibility measurements and various spectroscopic techniques. Each complex contains a cobalt(ii) center with a slightly distorted octahedral geometry and a second cobalt(ii) center with a distorted trigonal prismatic one. To obtain insight into the physical nature of weak non-covalent interactions, we have extensively used the Bader's quantum theory of atoms-in-molecules (QTAIM). In addition, the non-covalent interaction reduced density gradient (NCI-RDG) methods established the presence of such non-covalent intermolecular interactions. Variable temperature magnetic susceptibility measurements show that both cobalt centers in each complex are in the high spin state (S = 3/2) and both complexes show weak ferromagnetic couplings through the double phenoxido bridges (J = 3.36(3) cm-1 in 1 and 4.56(2) cm-1 in 2). The magnetic properties of both complexes can be fitted to a Co(ii) dimer model including similar orbital reduction factors (α = -0.94(1) for 1 and -0.85(1) for 2) although different zero field splitting parameters D(1) = 11.0(4) cm-1 and D(2) = 19.5(4) cm-1 in 1 and D(1) = 8.2(4) cm-1 and D(2) = -1.3(4) cm-1 in 2. AC magnetic measurements reveal that the CoII2 unit in complex 2 exhibits field-induced slow relaxation of the magnetization at low temperatures and high frequencies.