AN ACR B737 FLC DEPARTS; IN A RUSH; OVER THE WT LIMIT FOR THE RWY IN USE.

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AFTER LNDG AT GREER STATE ARPT WE WERE INFORMED BY THE TWR THAT THE ARPT WOULD BE CLOSED AT XA24 LCL TIME BECAUSE THERE WERE NO RWY OR TAXI LIGHTS WORKING AT THE TIME. WE LANDED AT XA13 LCL TIME AND WERE READY TO PUSH BACK FROM THE GATE AT XA33. WE WERE ALL WORKING HARD TRYING TO UNLOAD 137 PAX AND THEN RELOAD ANOTHER 137 PAX TO RETURN TO BWI. AT XA24 WE WERE TOLD THAT THE ARPT WAS OFFICIALLY CLOSED AND THERE WOULD BE NO MORE DEPS OR ARRS. I READ TO THE TWR OFFICIALS OUT OF OUR FLT OPS MANUAL THAT THE CAPT HAS THE OPTION TO DEPART FROM AN ARPT WITH INOP LIGHTING SYS AS LONG AS HE DETERMINES THAT THERE IS ADEQUATE AMBIENT LIGHT TO SAFELY CONTINUE THE TKOF. AFTER NEGOTIATING FOR SEVERAL MINS THE TWR CTLR AGREED TO LET US DEPART ON OUR OWN DISCRETION. HE SUGGESTED THAT WE USE RWY 16 FOR DEP TO EXPEDITE GETTING AIRBORNE. I ASKED MY FO IF WE COULD USE RWY 16 AT OUR TKOF WT AND HE SAID YES. HE WAS VERY BUSY TRYING TO GET EVERYTHING READY TO GO AND HE DID NOT THOROUGHLY CHK OUR MAX RWY WT. WE ROTATED FOR LIFTOFF WITH ABOUT 1500 FT OF REMAINING RWY. THE MAX WT WE SHOULD HAVE USED FOR RWY 16 WAS 114000 LBS. WE WERE AT 116700 LBS. THE CIRCUMSTANCES THAT PRECEDED OUR DEP WERE VERY HECTIC AND STRESSFUL AND CREATED THE URGENCY TO LEAVE ASAP. THOSE KIND OF CIRCUMSTANCES CAN CREATE THE SNOWBALL EFFECT WHICH CAN VERY EASILY LEAD TO AN ACCIDENT IF ANYTHING UNUSUAL GOES WRONG. I NEED TO BE ABSOLUTELY SURE THAT UNDER STRESSFUL AND HURRIED SITS THAT ALL DETAILS OF OUR FLT ARE DOUBLECHKED FOR POSSIBLE MISTAKES THAT CAN CREATE HAZARDOUS SITS.