In my opinion:
Best Weezer cover: I'm going to say "Velouria" by The Pixies.
Best Weezer cover from another band: It's tough, but I'm going to say Only In Dreams by Ash. Although I really enjoy Jack's Mannequin covering My Name Is Jonas. Most of the covers I've heard don't do it for me.
I think it would be You Might Think. It is just awesome!
Also in my opinion, no band can do a Weezer song well. I think they all stink.
I liked "Big Me", but out of their releases, I say Velouria.
I like Dashboard's version of Jamie, the String Quartet Tribute to Pinkerton, and Mock Orange's version of OID