Hero's sword and Jon Snow
Jon Snow getting a special heroic sword (Valyrian Steel with wolf themed pommel) could be a cliche fantasy trope. But Martin doesn't give his character a sense of glory. Jon doesn't feel happy or cheered but is instead haunted by his thoughts and situation.
His first thought is shame. He thinks he has no rights to it and rejects it.
Even then he had known it was only a child’s folly; no bastard could ever hope to wield a father’s sword. Even the memory shamed him. What kind of man stole his own brother’s birthright? I have no right to this, he thought, no more than to Ice. He twitched his burned fingers, feeling a throb of pain deep under the skin. “My lord, you honor me, but—”
Then he wishes it was his father who gave his sword to him, not Mormont. The father who is currently arrested for treason and his brother Robb who is marching, while he himself is sitting at the end of the world.
He knew he should be honored, and he was, and yet…
He is not my father. The thought leapt unbidden to Jon’s mind. Lord Eddard Stark is my father.
And just before this, Jon resents Mormont for lying to him.
And you tell me what you want me to know, and that’s less, Jon thought resentfully. His brother Robb had called the banners and ridden south to war, yet no word of that had been breathed to him…
When he shows his sword to his friends, he pretends to be proud.
“Valyrian steel,” he declared solemnly, trying to sound as pleased and proud as he ought to have felt.
He leaves his friends halfway, frustrated and angry.
His friends meant well, but they did not understand. It was not their fault, truly; they had not had to face Othor, they had not seen the pale glow of those dead blue eyes, had not felt the cold of those dead black fingers. Nor did they know of the fighting in the riverlands. How could they hope to comprehend?
To me, ASOIAF is grim because of these aspects as well. Heroic and epic, yes, but there's an eternal sense of grief and tragedy. Sadness was my constant companion while re-reading AGOT.