"Weight class" refers to a defined span of included weights. For instance, in the sport of wrestling participants spar with others of their own weight class so that the event is evenly matched. The weight classes may include wrestlers up to 106 pounds, over 106 but less than 113 pounds, over 113 but under 120, and so on.
As to the handle of the tub, your narrative does not provide enough information for an answer.