read between the lines

Probably from glosses and commentaries which were written between the lines and provided the reader with additional information not explicitly stated in the text.

• "If you read between the lines a little, you will realize that he has deeper motives."
• "The next day he made incantation, and distorted the miracle of the loaves and fishes till it became prophecy, and I, reading between the lines, saw that it was aimed at the wealth of meat stored in my caches."
• "“I’m quite of your opinion,” Miss Van Vluyck came briskly to her support; “on condition, that is, that all grossness of language is avoided.” “Oh, I’m sure we shall understand without that,” Mrs. Leveret tittered; and Laura Glyde added significantly: “I fancy we can read between the lines,” while Mrs. Ballinger rose to assure herself that the doors were really closed."
• "“Yes. And if you had as much sense as the talking parrot I owned once you would have read between the lines that all I wanted you here for was to tell you what I think of you.”"
• "I know you read between the lines / When them up there say it's all fine"
• "“Trust is as trust does. I tend to be extremely literal in what I say … One does not [need]^([sic]) to read between the lines. One can simply read the lines,” Musk said in the meeting, according to a tweet from Nola Weinstein, Twitter’s global head of brand experiences and engagement."
• "If you could see behind my eyes / You'd see the truth inside the lies / And if you read between the lines / You'd see I'm running from my mind"