Every person who operates a property-carrying vehicle for compensation over the highways of the Commonwealth shall be required to pay an annual fee of $10 for each such vehicle so operated, unless (i) such operation is exempted from this chapter; (ii) the property-carrying vehicle is a passenger car, motorcycle, autocycle, moped, or vehicle with a gross vehicle weight rating of 10,000 pounds or less; (iii) a vehicle identification marker fee has been paid to the Department as to such vehicle for the current year under the provisions of Chapter 27 (§ 58.1-2700 et seq.) of Title 58.1; or (iv) a fee has been paid for the vehicle through the unified carrier registration system established pursuant to 49 U.S.C. § 14504a and the regulations promulgated thereunder for carriers registered pursuant to those provisions. No more than one vehicle fee shall be charged or paid as to any vehicle in any one year under Chapter 27 (§ 58.1-2700 et seq.) of Title 58.1 and this chapter, including payments made pursuant to the unified carrier registration system.