B727 CREW; AFTER A WX DIVERSION; DEPARTED ARPT AFTER LCL CURFEW.

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DUE TO WX AT MIA WE HAD TO DIVERT. FIRST ALTERNATE WAS FLL; SECOND WAS PBI; PER FLT PLAN. AFTER RADIO CALL TO DISPATCH; I INFORMED THEM THAT AT BINGO I WOULD BE GOING TO PBI SINCE CONDITIONS APPEARED BETTER. WHILE ON OUR WAY TO PBI; DISPATCH SENT ACARS MESSAGE ASKING US TO GO TO FLL. DUE TO WX; I DECIDED TO GO TO PBI PER OUR VOICE CONVERSATION. WHAT I DID NOT KNOW WAS THAT THERE WAS A CURFEW FOR NON STAGE 2 ACFT AFTER XX30 AS PUBLISHED IN PART 2 DEP SECTION. DUE TO WORKLOAD; WE DID NOT REVIEW THIS INFO AND DISPATCH DID NOT VOLUNTEER IT ALSO. AFTER LNDG; DISPATCH MGR SAID JUST TAKE OFF AND WE WILL WORRY ABOUT IT LATER; WHICH IS WHAT WE DID. I AM CONCERNED ABOUT TAKING OFF AGAINST CURFEW AND WHY PBI WOULD BE LISTED AS AN ALTERNATE WHEN IT WASN'T SUITABLE. SUPPLEMENTAL INFO FROM ACN 416756: DIVERTED TO PBI DUE TO WX AT MIA AND LOW FUEL. AFTER LNDG AT PBI AND REVIEWING DEP INFO; WE BECAME AWARE OF A TKOF CURFEW FOR B727'S. WE CALLED DISPATCH AND ASKED IF THEY COULD OBTAIN A WAIVER; WHICH THEY SENT VIA ACARS. WE CALLED TWR ALSO TO COORDINATE A WAIVER AND THEY CALLED US BACK A FEW MINS LATER WITH A CLRNC FOR DEP.