The answer to the riddle: "Forward I'm heavy; backwards I'm not" is a ton. A ton spelled backwards is "not"; therefore, while a ton is heavy, in actuality weighing 2,000 pounds, when just looking at the word instead of the thing itself ,it becomes the word not backwards.
This riddle falls into a common category of "What am I?" riddles where one receives details about an item and has to puzzle out what the item is. Another common riddle in this category is "I am the beginning of every end and the end of every race" to which the answer is the letter e. Frequently these types of riddles play with language.