Can someone become cross-eyed if they damaged their eyes by reading at night or so?

No: Using your eyes will not cause eye disease.

Eye Don't Think So: I suppose if you held a book in each hand and tried to read the book on the right with your left eye and the book on the left with your right eye, you might have a problem.But otherwise, assuming normal eye innervation and coordination and proper posture and lighting, reading at night should nor pose a problem unless it's at the computer or tablet.That's a whole other thing: eyestrain, fatigue,etc