Every such bridge shall be constructed by contract with the commissioners of both the said counties; it shall be inspected, in the manner aforesaid, by persons appointed by the court of quarter sessions of either of the said counties; it shall be paid for, maintained, and kept in repair by said commissioners, the cost and expense of which joint construction, maintenance, and repair shall be paid by said counties, respectively, in the proportion of the population thereof as ascertained at the last decennial census, and if either county shall necessarily incur more than its due proportion of such charge, it shall be lawful for such county to recover from the other county the excess so incurred, and in an action to be founded on this act: Provided, This shall apply only to counties having a population of two hundred thousand and under, and, in such counties, to bridges three hundred feet (300) in length and over.