Orcrist

[lathspell]

The actual quote from the Hobbit runs thus:

Actually is was some days before Bilbo really set out. They buried Thorin deep beneath the mountain, and Bard laid the Arkenstone upon his breast.
"There let it lie till the mountain falls!" he said. "May it bring good fortune to all his folk that dwell hereafter!"
Upon his tomb the elvenking then laid Orcrist, the elvish sword that had been taken from Thorin in captivity. It is said in songs that it gleamed ever in the dark if foes approached and the fortress of the dwarves could not be taken by surprise.

So it seems clear that the Arkenstone was lain upon his breast by Bard. Thranduil did indeed lay Orcrist on his tomb. Another point is the rumour about the songs in which it was said that Orcrist gleamed if foes approached the mountain. I mean, why sing anything like it if you can't see the blade anyway? It is, I think, a heartening thought after all the dealings with Smaug that you wouldn't have to worry anymore about such things, because if another Dragon came from the north the sword would gleam. Wether the story is true... who knows?

Now, back to the original question of this thread. Why didn't Dain fight with Orcrist?
If I remember correctly, in mythology dwarves generally are very reluctant to use one another's tools. There most beloved tools for crafting or weapons in battle were therefore not lightly used by another dwarf. I do not know if Tolkien used this dwarven characteristic in his books, but it might be. Then Dain wouldn't have taken Orcrist from Thorin's tomb, unless he had no other choice.
Another reason could be that what Orcrist was for Thorin, Dain's axe was for him. It is said in UT that Dain wielded his axe with great power. Maybe he had a greater power when fighting with his axe then with Thorin's sword. It is like Aragorn and Anduril. Anyone can carry Anduril and stab an orc with it, but Aragorn is the only one who van actually wield the power of the sword.

greetings,
lathspell