Canon says that the Elves and Dwarves made peace (of a sort - they still didn't like each other much) after the initial unfortunate incidents, but it doesn't really explain how that happened. The Dwarves asking for weregild is thus my own interpretation. I'm not sure Elves really understand the concept of money at this stage, hence Thingol's confusion at the end.
Also, does the US President know that his first name is Dwarvish for 'Axes'?
Part 108: Baruk Khazâd!
Next time: Part 109: The world was young
Chibis by tektek.org