You're right - I was too hasty. It's not 再来週.

Are you sure about "the week after next"? To me, that means two weeks from *now* (which is 
what 次々週 means, but not 翌々週, I believe). 
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It's my understanding (perhaps I'm wrong) that 翌々週 means two weeks from *then* (i.e. from 
some point in the past or future, but not from *now*).
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Certainly, 翌週 is defined in EDICT as "the following week; the next week" rather than "next 
week", which would mean "one week from *now*".
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Similarly, Shogakukan defines 翌週 as "the next [following] week" and not as "next week" (the 
"the" makes a significant difference to the meaning).
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And Kojien says 翌週 means その次の週 and not simply 来週.
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At the following reference, is defined as "two weeks later", which is what I would have 
expected, and matches "the week after the following week" but not "the week after next".
http://www.jlogos.com/new2_result2.html?id=7720272&word=翌々週
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Kojien also has 翌翌年 = 翌年の翌年。その次の次の年。 and not simply 再来年.
Kojien also has a similar entry for 翌翌日.
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In EDICT, 翌翌日 = "two days later; next day but one" and NOT as "the day after tomorrow".
However, EDICT says 翌翌年 = "two years later; year after next" and I think that's incorrect.
It should be "two years later; the year after the following year", I believe
(based on Kojien's definition.)

@@ -13,1 +13,2 @@
-<gloss>the week after next</gloss>
+<gloss>two weeks later</gloss>
+<gloss>two weeks after that</gloss>

@@ -13,0 +13,1 @@
+<gloss>the week after next</gloss>

http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1239667352