Why were snapes last words look at you?

Answer 1

For starters, Snape was not pleading with Harry to understand him or his motivations. Snape is a man who is hardly afraid of being hated or misunderstood. And he wasn't just giving Harry his marching orders for the showdown with Voldemort. He could have done that without showing Harry all of those embarrassing memories of Lily.

Instead, Snape was finally acknowledging, for the first time to Harry at least, that Harry Potter was Lily's son too - not just James's son - and that he himself (Snape) bore a great deal of responsibility for destroying his childhood friendship with Lily. Snape is a proud man who chooses in his last moment to humble himself. With these memories, he acknowledges his own culpability, his own sin. He is finally revealing that he was not just an innocent victim of mean James Potter and the other Marauders.

The key to this reading is that Snape freely gives Harry his worst school memory - the same memory that Harry stole a peak at after an Occlumency lesson. Harry's unearned look into the Pensieve had egregiously violated Snape's privacy, infuriating the Potions Master. But Snape seemingly forgives Harry here, not only giving him the complete memory, but revealing to Harry the ultimate consequences of young Snape's own actions.

Harry already knows that Snape called his mother a mudblood when she rushed to defend him. But Harry had not previously seen Lily confront young Severus with the fact that he was now calling every muggle-born a mudblood. Yes, Harry probably suspected it, given Snape's Death Eater past, but Snape himselfchooses to reveal it to his least favorite pupil. And what does he reveal? That it was young Snape's corruption by the pure blood ideology - despite being a half-blood like Harry and Dumbledore - that destroyed a long friendship with Harry's mother.

Yes, you can read "Look at me" as nothing more than the desire to gaze into Lily's eyes as he dies. Lots of Snape haters do. But given everything Snape shows Harry, it's more likely IMO that he's finally acknowledging, to Harry, that Harry is, as Dumbledore told him, his mother's son. He is not responsible for the sins of his father. He has his mother's eyes.