Talking about the "weariness" itself... the weltschmertz or the angst...
Well, blaming Sauron for it looks to me a bit too simple an answer - and not honouring the elves their due. Like, "I'm getting done with your rule in the ME, now start feeling bad and show some common resignation"...
Looking at Tolkien's work one should probably look farther and on a larger scale.
What I have always thought being the reason for the "annui" has been just the fact that they have lived so long, being involved for so long, seen so much... seen so many a thing recurring, repeating itself.
Every child - or a childish person - wants to live forever but when one gets even a glimpse of what eternity might actually mean one grows up and sees the freedom and meaningfulness of living a limited mortal life. To me that has just been the realisation of the elves... they have grown up, they have realised that another millenia, and another, and another... will be just the same with some minor variations and the struggle between good and bad etc. will go on whatever they do...
And isn't that one of the recurring themes of our mythologies and popular cultures: how immortals envy those who can just live and die?
That might be just my perspective but I think one could actually argue for it, at least better than for Sauron and the fear of losing control...
