I am looking for resources to progress in Latin reading. In particular, I would like a set of texts (for example short stories or fables) whose difficulty increases as you go along.
A very good option would be A Little Latin Reader by Mary C. English and Georgia Irby-Massie.
The Bryn Mawr Classical Review had the following to say about it:
In 50 short chapters, English and Irby have assembled over 200 passages (2-10 lines in length) of authentic Latin arranged in order of increasing difficulty of the grammatical or syntactical concept being emphasized. In Chapters 1-46, passages are drawn from Caesar, Catullus, Cicero, Horace, Livy, Martial, Ovid, Tacitus, and Vergil and from Latin inscriptions that treat aspects of daily life in the Roman world.