I just saw an interesting interpretation of Galadriel's gift to Gimli on Reddit today, I retraced the source of the image to this tumblr post:
If you’ve read the Silmarillion, you know who Fëanor was. If you don’t, Fëanor was the dickhead who created the Silmarils: three indescribably beautiful and magical jewels that contained the light and essence of the world before it became flawed. They were the catatlyst for basically every important thing that happened in the First Age of Middle Earth.
It is thought that the inspiration for the Silmarils came to Fëanor from the sight of Galadriel’s shining, silver-gold hair.
He begged her three times for single strand of her beautiful hair. And every time, Galadriel refused him. Even when she was young, Galadriel’s ability to see into other’s hearts was very strong, and she knew that Fëanor was filled with nothing but fire and greed.
Fast forward to the end of the Third Age.
Gimli, visiting Lorien, is also struck by Galadriel’s beauty. During the scene where she’s passing out her parting gifts to the Fellowship, Galadriel stops empty-handed in front of Gimli, because she doesn’t know what to offer a Dwarf. Gimli tells her: no gold, no treasure… just a single strand of hair to remember her beauty by.
She gives him three. Three.
And this is why Gimli gets to be an Elf Friend, people. Because Galadriel looks at him and thinks he deserves what she refused the greatest Elf who ever lived—and then twice* that. And because he has no idea of the significance of what she’s just given him, but he’s going to treasure it the rest of his life anyway.
Just look at that smile on Legolas’s face in the last panel. He gets it. He knows the backstory. And I’m pretty sure this is the moment he reconsiders whether Elves and Dwarves can’t be friends after all. [source]
I didn't finish The Silmarillion, so I wonder; is that true? Did Tolkien confirm this interpretation?
*: "twice" is in the source being quoted here; "three times" of course would be the correct amount but "twice" is retained to preserve the quote.