Is the permissibility of eating food with worms and weevils, due to the difficulty of avoiding them, based on a text or an authentic narration, or on juristic reasoning? And what is the standard for the considered difficulty?

There is no authentic text from the Sunnah regarding the ruling on dates containing weevils. The issue is one of ijtihad (independent reasoning), and the opinions of the jurists regarding it are based on general principles such as lifting hardship (raf‘ al-haraj) and bringing ease (jalb al-taysīr) when there is difficulty. The recognized difficulty is that which is deemed a hardship by common custom.