The governing body of any city may adopt ordinances providing weight limits in accordance with the weight limits established by §§ 46.2-1123 through 46.2-1127 for any vehicle or combination of vehicles passing over any such roads under the jurisdiction of such city, and providing further for the assessment of liquidated damages as to overweight vehicles at rates and amounts not exceeding those applicable to the liquidated damages under § 46.2-1135. Such ordinances may provide: Upon a finding of a violation of any weight limit prescribed therein, the court shall assess the owner, operator or other person causing the operation of such overweight vehicle at such rate and amount as may be provided in such ordinance; The assessment shall be entered by the court as a judgment for such city; The entry of such judgment shall constitute a lien upon the overweight vehicles; Such sums shall be paid into the treasury of such city, and allocated to the fund appropriated by such city for the construction and maintenance of such roads under its jurisdiction. Such ordinances may include additional provisions relating to payment of such assessment and enforcement powers applicable to such city and corresponding to the provisions of §§ 46.2-1131, 46.2-1133, 46.2-1134 and 46.2-1135, except that civil penalties, liquidated damages and weighing fees collected pursuant to such ordinances shall be paid to the city, and the city attorney or his designee shall represent the city in any court proceeding.