Seven acentric sulfides Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi, Sn) were grown by a high-temperature salt flux method. The crystal structures of the Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi, Sn) compounds were determined by single-crystal X-ray diffraction with the aid of solid-state NMR spectroscopy. The Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi) compounds are isostructural and crystallize in the Ba6Ag4Sn4S16 structure type. The Sn-containing compound exhibits high structural similarity to Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi) with the presence of an interstitial atomic position partially occupied by Sn atoms. The chemical bonding characteristics of Ba6(Cu2.9Sn0.4)Sn4S16 were understood with electron localization function calculations coupled with crystal orbital Hamilton population calculations. The Ba-S and Cu-S interactions are dominantly ionic, but the Sn-S interactions consist of strong covalent bonding characteristics in Ba6(Cu2.9Sn0.4)Sn4S16. The monovalent Cu atoms, mixed with certain metals with various oxidation states, significantly shift the optical properties of the Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi) compounds. This results in a good balance between the second-harmonic-generation (SHG) response and laser damage threshold (LDT). Ba6(Cu1.9Zn1.1)Sn4S16 possesses a high SHG response and a high LDT of 2.8 × AGS and 3 × AGS, respectively. A density functional theory calculation revealed that CuS4 and SnS4 tetrahedra significantly contribute to the SHG response in Ba6(Cu2Mg)Sn4S16, which also confirmed that CuS4 tetrahedra are crucial for the stability and optical properties of the Ba6(CuxZy)Sn4S16 (Z = Mg, Mn, Zn, Cd, In, Bi, Sn) compounds revealed by electronic structure analysis.