With insights into the context and story from Contemplatebooks.com.

Excerpt:

"But even yet I refrained and kept still. I scarcely breathed. I held the lantern motionless. I tried how steadily I could maintain the ray upon the eye. Meantime the hellish tattoo of the heart increased. [He treats stillness as mastery, the sound grows anyway. Control fails.] It grew quicker and quicker, and louder and louder every instant. The old man’s terror must have been extreme! [Projection, he describes his own rising fear.] It grew louder, I say, louder every moment!—do you mark me well? I have told you that I am nervous: so I am. [He admits nervousness while still pressing the sanity case, a contradiction he cannot hear.] And now at the dead hour of the night, amid the dreadful silence of that old house, so strange a noise as this excited me to uncontrollable terror. [Silence becomes an amplifier, his mind fills it.] Yet, for some minutes longer I refrained and stood still. But the beating grew louder, louder! I thought the heart must burst. And now a new anxiety seized me—the sound would be heard by a neighbour! [Social exposure is the true fear, this is why darkness feels therapeutic to him.] The old man’s hour had come! With a loud yell, I threw open the lantern and leaped into the room. He shrieked once—once only. In an instant I dragged him to the floor, and pulled the heavy bed over him. I then smiled gaily, to find the deed so far done. [Elation at control, the high after the act.] But, for many minutes, the heart beat on with a muffled sound. This, however, did not vex me; it would not be heard through the wall. [Denial, he talks himself down.] At length it ceased. The old man was dead. I removed the bed and examined the corpse. Yes, he was stone, stone dead. I placed my hand upon the heart and held it there many minutes. There was no pulsation. He was stone dead. His eye would trouble me no more. [He thinks he killed the gaze that judged him. The story will prove him wrong.]"

That last line — “His eye would trouble me no more” — is the narrator silencing judgment. The “eye” represents whatever he feels watching him — a parent, God, society, or even his own conscience. It’s the gaze that sees too much, the part of life that reminds him he’s small, flawed, exposed. By destroying it, he’s quieting the feeling of being seen and judged that has afflicted his soul for too long.