Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. Co3Sn2S2 is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of Co3Sn2S2 using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green’s function methods. Co3Sn2S2 exhibits highly anisotropic magnon dispersions and linewidths below TC, and paramagnetic excitations above TC. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor “across-hexagon” Jd model. Our density functional theory calculations reveal that both the symmetry-allowed 120° antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role Co3Sn2S2 can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.