I'd be astonished if they did.
There may have been a case for CFAA violation (right or wrong), but the prosecutors improperly chose New Jersey as the venue of proceedings. This was a calculated move that had the effect of producing additional state charges, which then resulted in an increased Federal charge for CFAA + State Law violations. That sort of willful "venue shopping" cuts both ways, then; as soon as they try for additional charges, prosecutors now had to conclusively prove that the location of venue was material to the crime at hand, as well as the actions committed.
Since Weev &co were not in NJ at the time the act occurred, and neither were the machines they accessed, and there's no conclusive proof of NJ residents being harmed, then the venue of crime committed was incorrect and thus so were the additional charges hung on it. And that is the prosecutorial misstep which was overturned on this appeal, which is subject to jeopardy limitations.
http://criminal.findlaw.com/criminal-rights/when-double-jeop...
The case on point is United States v. Ball, 163 U.S. 662 (1896)* which rejects the English common law rule that holds the opposite. Frankfurter's dissent in Green v. United States, 355 U.S. 184 (1957)+ is far easier to read and lays out the history well.
* http://scholar.google.com/scholar_case?case=2223826737867114...
+ http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=case&...
Still, the prosecution is really unlikely to do so.
He had his conviction overturned by SCOTUS. The state then retried him and convicted him.
http://criminal.findlaw.com/criminal-rights/charged-twice-in...
"But if a single act violates the law of two states, the law treats the act as separate offenses and thus not in conflict with the Double Jeopardy Clause. A second state with a case against a defendant may decide that a conviction in the first state is sufficient, so it does not necessarily mean more than one state will bring charges. Therefore, it is up to the discretion of the particular prosecutor, as with other criminal cases."
This is known as the Dual Sovereignty Doctrine. This is also what makes hacking such a perilous crime. If you're hacking a large corporation in one state, you may have victims in multiple states. Thus, you can be tried separately for essentially the same crime in multiple states regardless of being acquitted in other states.
No, because this wasn't a prosecution under NJ law, it was a prosecution under federal law, in which the violation of NJ was an element of the offense. So double jeopardy prevents any further federal prosecution for the same offense, but doesn't prevent prosecution under state law of NJ or other states (even though the court here found NJ law did not apply, federal circuit court precedent on state law questions is not binding on state courts.)
This avoids any serious ruling about CFAA, and preserves the arbitrarily-expansive reading of CFAA to use against other victims. They've already ruined weev's life sufficiently for their purposes.