The mayor and city council of any city of the second class, or the board of trustees of any village, are hereby authorized to lay off such city or village and the territory within the extraterritorial zoning jurisdiction of such city or village into suitable districts for the purpose of establishing a system of sewerage and drainage. Such city or village may (1) provide such system; (2) regulate the construction, repairs, and use of sewers and drains and of all proper house connections and branches; (3) compel all proper connections therewith and branches from other streets, avenues, and alleys, and from private property; and (4) provide penalties for any obstruction of or injury to any sewer or part of such sewer or failure to make connections with such system.