The Commissioner, upon written application by Arlington County, shall issue without a fee to such county a permit authorizing the county’s operation of vehicles used for hauling household waste and vehicles used for highway or utility construction, operation, or maintenance upon the highways of such county at gross weights exceeding those set forth in § 46.2-1126. Permits issued hereunder shall specify that vehicles with two axles may have a maximum gross weight of no more than 48,000 pounds and a single axle weight of not more than 24,000 pounds and that vehicles with three axles may have a maximum gross weight of not more than 60,000 pounds and a single axle weight of not more than 24,000 pounds and a tandem axle weight of not more than 40,000 pounds. The permit shall not designate the route to be traversed nor contain restrictions or conditions not applicable to other vehicles in their general use of the highways. Each vehicle, when loaded according to the provisions of a permit issued under this section shall be operated at a reduced speed of 10 miles per hour slower than the legal speed limit in 55, 45, and 35 miles per hour speed limit zones.