It shall be the duty of such commissioners to examine the locality where the improvement is proposed to be made and the property which will be especially benefited thereby, and to estimate what proportion, if any, of the total cost of such improvement will be a benefit to the public, and what proportion thereof will be a benefit to the property to be benefited, and apportion the same between the city and such property so that each shall bear its relative equitable proportion, and having found said amounts, to apportion and assess the amount so found to be a benefit to the property upon the several lots, blocks, tracts and parcels of land, or other property in the proportion in which they will be severally benefited by such improvement: PROVIDED, That the legislative body of the city may in the ordinance initiating any such improvement establish an assessment district and said district when so established shall be deemed to include all the lands or other property especially benefited by the proposed improvement, and the limits of said district when so fixed shall be binding and conclusive on the said commissioners: AND PROVIDED FURTHER, That no property shall be assessed a greater amount than it will be actually benefited. That all leasehold rights and interests of private persons, firms or corporations in or to harbor areas located within the corporate limits of any incorporated city or town are for the purpose of assessment for the payment of the awards, interest and costs of any improvement authorized by this chapter, declared to be real property, and all such leasehold rights and interests may be assessed and reassessed in accordance with the special benefits received for the purpose of paying the cost of any such improvement heretofore made or which may hereafter be made in accordance with law.