DC9 CREW BECAME TRAPPED IN THE FAR FUEL REQUIREMENTS BY CHANGING DEST ARPTS.

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ABOUT 20 NM E OF PMM VOR (DEPARTED FROM IAD) CTR INFORMED US THAT MKE ARPT WAS CLOSING DUE TO TSTMS AND WE WERE TO HOLD AT PMM. WHILE IN THE HOLD WE DECIDED WE COULD DEVIATE N OF TVC THEN GRB THEN S TO MKE AND GET BEHIND THE LINE OF STORMS. WE TALKED TO DISPATCH AND THEY AGREED AND GAVE US WX AT GRB AND ATW (ON BACK SIDE OF LINE). WE LEFT THE HOLD WITH 11000 LBS OF FUEL. AS WE PROCEEDED NEBOUND THE LINE INTENSIFIED OVER LAKE MICHIGAN AND STARTED PUSHING EBOUND RATHER QUICKLY. THIS PUT US FURTHER E THAN WE ANTICIPATED. WHEN WE TURNED WBOUND WE ENCOUNTERED STRONG HEADWINDS. WE TALKED TO DISPATCH AT THAT POINT AND TOLD THEM THAT WE WOULD LIKE TO CHANGE OUR DEST TO GRB. THEY AGREED AND CHANGED IT. THE WX IN GRB WAS SUCH THAT I NEEDED AN ALTERNATE. WITH DEST ALTERNATE AND 45 MINS RESERVE WE WERE UNDERFUELED BY 400 LBS. THIS WOULD DIP INTO THE RESERVE. WE DECIDED THIS WAS THE SAFEST COURSE OF ACTION RATHER THAN TURN BACK E AND GO SOMEWHERE ELSE. THE RAPIDLY CHANGING WX WAS THE MAJOR CONTRIBUTING FACTOR ALONG WITH THE VERY STRONG HEADWINDS ENCOUNTERED WHILE PASSING AROUND THE LINE. AN EARLIER DEV OR DIVERSION SOMEWHERE ELSE MAY HAVE PREVENTED THIS; BUT WHEN WE STARTED THE DEV AROUND THE TSTMS THIS LOOKED LIKE A VIABLE RTE.