Torque and weight are effected by an object's balance. If you have an object like a book, and it is set on a table, the object is at balance. This means the object's weight is supported in a way that no torque is required to hold it where it is.
Understanding geometric center is another important factor to torque and weight. When an object has its weight distributed equally through the entirety of its physical body, its center of gravity is located in its geometric center. When an object's weight is unequally distributed, the center of gravity is most likely not at its geometric center. If the object's weight is acted upon at its geometric center, it needs less torque to move. Likewise, if you don't exert the torque at the geometric center, the force needed to move the object is greater, meaning the weight of the object feels greater.
To lift a 5-lb. dictionary from the edge of a table by lifting the book from it's edge, you must exert more torque to lift the book by its edge. Since the dictionary's geometric center is in the middle of the book, the force needed to lift the book is much more than the 5-lb. weight of the dictionary.
To counteract this extreme increase in force, lift the book as close to its equilibrium center as possible. This makes the net torque exerted as close to the actual weight of the book as possible. At perfect balance, you only need to exert 5 lbs. of torque to lift the book, which weighs 5 lbs.