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1.
When you're so burned out by all you've had to do Monday through Friday that you just want to party, watch TV, etcetera the whole weekend and are unwilling to do anything important.

In extreme cases, you might be so tired that you end up wasting the entire weekend by doing things that are not only unproductive, but not even particularly interesting.
JOE: Hey what'd you do this weekend?
STEVE: Saw two movies, partied, did nothing important had fun.
JOE: Well, it was a long week, so I guess weekend syndrome is okay.
BOB: I basically spent the whole weekend playing solitaire, watching random YouTube clips, and reading random trivia on Wikipedia. So not only did I waste the whole weekend, but I didn't even waste it on anything particularly interesting.
STEVE: Dude, that's extreme weekend syndrome. What the frick did you have to do during the week?
by Daedalus Suburbanus September 28, 2010
 
2.
when you choose not to give a fuck about anything on the weekend because the week was either to long or you are extremely hungover
Mike: Hey June
June: Hey Mike, how was your weekend?
Mike: My weekend was awesome until I came down with a really bad case of weekend syndrome
June: Dam, sorry to hear that Mike
by The Real M. Jackson November 23, 2013