FLT CREW OF B733 DEPARTED WITH TKOF GROSS WT IN EXCESS OF MAX ALLOWABLE TKOF GROSS WT AGREED TO ON DISPATCH RELEASE.

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WHILE CALCULATING THE TKOF DATA INTO THE ONBOARD PERSONAL COMPUTER; I NOTICED THAT THE ATOG OF 115.8 WAS GREATER THAN THE MAX ATOG AVAILABLE ON THE DUTY RWY AT MIDWAY; WHICH WAS RWY 4R. I INFORMED THE CAPT OF THIS AND HE ASKED ME TO CHK RWY 31C BLEEDS ON; AND RWY 4R AND RWY 31C BLEEDS OFF; WHICH ALL GAVE AN ATOG GREATER THAN OUR DISPATCH RELEASE ATOG OF 115.8. THE CAPT INDICATED THAT HE WOULD INFORM THE OPS AGENT OF THIS AND HE WOULD TAKE CARE OF IT; IF WE DID IN FACT NEED THE EXTRA FOR THIS FLT. WHEN THE OPS AGENT GAVE US THE LOAD SHEET; WE WERE NOW RUNNING 30 MINS LATE; AND THE TKOF WT LISTED ON THE LOAD SHEET WAS 200 LBS GREATER THAN OUR ATOG OF 115.8. I POINTED OUT TO THE CAPT THAT WE WOULD HAVE THE REQUIRED ATOG AVAILABLE FOR RWY 4R IF WE USED 'BLEEDS OFF' FOR THE CURRENT WX ON THE ATIS. OUR TKOF WT ON THE LOAD SHEET WAS 116.0 AND THE ATOG LIMIT FOR RWY 4R 'BLEEDS OFF' WAS 117.6. I ASSUMED THAT THE CAPT HAD TAKEN CARE OF USING THE INCREASED NUMBER FOR ATOG CALCULATIONS WITH DISPATCH; AND THAT THE OPS AGENT HAD FORGOTTEN TO ANNOTATE THIS ON THE LOAD SHEET. THE 117.6 NUMBER WAS USED IN THE OPC AND GOOD TKOF DATA WAS CALCULATED FOR TKOF ON RWY 4R. BECAUSE WE WERE RUNNING SO LATE AND THE OPS AGENT WAS FRAZZLED; I DIDN'T TAKE THE TIME TO ASK MORE QUESTIONS AND DO A BETTER JOB OF BACKING THE CAPT UP. IF WE HAD SLOWED DOWN; I WOULD HAVE REALIZED THAT THE CAPT HAD NOT RECEIVED DISPATCH'S BLESSING TO USE THE GREATER ATOG VALUE THAT THE CURRENT WX CONDITIONS AT MDW GAVE US. IN THE FUTURE; I WILL ALWAYS DOUBLECHK AND AVOID THIS PROB HAPPENING EVER AGAIN.