Nature/Cause of the weariness of Eldar in the Third Age

[Inziladun]

I've always thought the 'fading' of the Elves in Middle-earth was connected to their inherent difference from the land itself. They were immortal creatures living in a mortal world, and eventually had to make way for the mortal Men who were its masters.
It seems to be a mirror effect of that which the Blessed Realm would have on mortals, as explained to the Númenóreans by the Eldar:

For it is not the land of Manwë that makes its people deathless, but the Deathless that dwell therein have hallowed the land; and there you would but wither and grow weary the sooner, as moths in a light too stong and steadfast.

Silm Akallabêth