Which box is the heaviest? 

Box P is heavier than at least two boxes. Box S is heavier than box R and box Q but not the heaviest. Number of boxes heavier than box S is equal to number of boxes lighter than box T. Box Q is heavier than box P. Box Q is not the 3rd heaviest box. Box V is heavier than box U which is lighter than box T. So, box S and box T must be 2nd heaviest and 2nd lightest boxes respectively. Also, As, box Q is not the 3rd heaviest, so, R must be 3rd heaviest and V must be heaviest box. The arrangement is shown below, V > S > R > Q > P > T >. U