To *stop* reading means: you decided to stop voluntarily, and not because of other factors, such as you have other works, sleepy, etc.
In other words, you stop because you feel bored of reading, or decide to read at another time.

Or are you a person who will just continue reading non-stop until there are other factors that forced you to stop, such as the library is closing, its already dark outside, you feel hungry, etc.