B737 FLT CREW EXECUTES A TKOF WITH THE ACFT EXCEEDING THE RWY LIMIT FROM ORD.

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THIS WAS A TYPICAL 'RACE' TO GET DEPARTED PRIOR TO TSTMS ARRIVING. THERE WERE CUMULONIMBUS BOTH N AND W OF ORD; AND ONLY SE DEPS WERE GOING. MANY AIRPLANES SITTING ON TXWYS AND RAMPS. WE WERE HUSTLED DOWN TXWY D TO RWY 22L FOR DEP. THE WX WAS APCHING QUICKLY FROM THE N; AND WAS OVER RWY 27R; 'N SIDE OF FIELD' AS WE APCHED RWY 22L. THE SKY WAS BLACK AS NIGHT. BUT S WAS CLR; AND A RWY 22L WITH A L TURN; (STANDARD DEP FOR ORD-BOS) LOOKED OK. THE WIND WAS PICKING UP AS WE WERE CLRED FOR TKOF; AND I THOUGHT THE TWR SAID THE WIND WAS 270 DEGS VERSUS 340 DEGS AT 16 KTS. I CHANGED MAX PWR; TAILWIND; AND TOLD FO TO CONTINUE TKOF. WE HAD A JUMP SEAT RIDER WHO LATER TOLD US THE TWR ANNOUNCED THE WIND AS 020 DEGS AT 20 KTS AS WE STARTED ROLL. I EITHER DIDN'T HEAR THIS OR DIDN'T REGISTER IT. TKOF PERFORMANCE WAS SOMEWHAT DEGRADED; DEFINITELY A TAILWIND. WE ROTATED AT THE 2000 FT TO GO MARKER AND BROKE GND WITH ABOUT 1000 FT TO GO. ALTHOUGH THE MAX PWR COVERED THE TAILWIND RESTR; AND WE WERE BELOW THE TAILWIND LIMIT; I NEVER THOUGHT ABOUT THE RWY LIMIT PENALTY WITH A TAILWIND. THE PENALTY WAS 1300 FT PER KT. WE LATER DETERMINED THAT AT THE WIND OF 340 DEGS AT 16 KTS; WE WERE 8400 LBS OVER THE RWY LIMIT. OBVIOUSLY AT 020 DEGS AT 20 KTS; IT WAS EVEN MUCH MORE. I DON'T KNOW WHAT I WAS THINKING. THIS WX WAS MOVING SO FAST THERE IS NO WAY THAT THE TKOF SHOULD HAVE BEEN COMMENCED. IT WAS BLACK AND IT WAS GUSTY AND I WAS THINKING OF GETTING THE JOB DONE; GETTING HOME; AND GETTING THE PEOPLE OUT OF ORD BEFORE THE WX HITS; AND SAFETY WAS COMPROMISED.