: In ancient societies such as the Egyptians or Viking-age Norse grave goods were meant to be of use to the dead in the afterlife.

: What use would a bow be to an Elvish soul in the Halls of Mandos?

: Also, as the barrows on the Barrow Downs were originally the graves of the Dunedain nobility of Cardolan (who would have believed in Eru), would they have thought that armour, weapons and jewels might follow a human soul beyond Arda?

: Perhaps this shows a little inconsistency in Tolkien's "Sub-creation"? Lavish burials smack of the heroic, as in Beowulf, but seem odd in a monotheist setting. Can you have Christ and Odin at the same time?

You raise some interesting ideas. I don't see why it would be important to bury Beleg's bow with him. But maybe its a part of the grieving process. You put the goods into the grave because you want them to be with that person. And somewhere along the way it becomes a belief that they will be with him.