B757 FLC DIVERTS DUE TO EMER LOW FUEL STATE.

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ENRTE TO MDW; WE WERE GIVEN A HOLDOVER AT MOLINE FOR ABOUT 25 MINS. WE HAD SUFFICIENT FUEL; AND CONTACTED DISPATCH. OUR ALTERNATE WAS KIND; THEY TOLD US TO KEEP THEM ADVISED. THERE WERE NUMEROUS TSTMS IN THE CHICAGO AREA THAT WERE CREATING THE PROB. WE WERE THEN CLRED OUT OF HOLDING VIA DIRECT PLL -- DPA -- MDW; AND TOLD TO DSND TO 5000 FT APPROX 130 MI FROM MDW. CTR SLOWED US TO 250 KTS AND HANDED US OVER TO ROCKFORD APCH. WE WERE NAVING BTWN LINES OF WX -- ONE TO THE N AND THE OTHER TO OUR S POS. WE WERE LOOKING AT LNDG IN MDW WITH ABOUT 10000 LBS OF FUEL; WHICH IS SUFFICIENT. WE WERE HEADED SE TOWARDS JOT; APPROX 75-80 MI FROM MDW WHEN APCH TOLD US TO BASICALLY DO A 180 DEG; BECAUSE CHICAGO WAS NOT GOING TO ACCEPT ANY MORE ACFT. HE GAVE US NO FURTHER INSTRUCTIONS AS TO WHAT TO DO OR EXPECT. WE WERE TOO FAR AWAY TO MAKE IT TO OUR ALTERNATE WITH OUR CURRENT FUEL. THE CAPT THEN DECLARED AN EMER FOR FUEL. WE ATTEMPTED TO MAKE AN APCH INTO ROCKFORD; ILLINOIS; BUT HAD TO BREAK OFF THE APCH; BECAUSE OF SEVERE WX. THE CTLR SUGGESTED JVL; WHICH WAS ABOUT 35 MI FURTHER N OF ROCKFORD. WE DID NOT HAVE THE COMMERCIAL PLATES FOR JANESVILLE; SO THE CTLR GAVE US THE RELEVANT INFO FOR THE ARPT AND THE ILS TO RWY 4. WE BROKE OUT ABOUT 800 FT AND LANDED WITHOUT INCIDENT WITH ABOUT 7000 LBS OF FUEL. BTWN THE WX AND EMER; WE DID NOT HAVE TIME TO CONTACT DISPATCH. I FEEL THIS SIT COULD HAVE BEEN AVOIDED IF CHICAGO DID NOT ACCEPT MORE ACFT THAN IT THOUGHT OR KNEW IT COULD HANDLE. I HAVE NEVER HAD TO HOLD AND THEN BE CLRED INTO MY DEST; AND THEN BE TOLD WE COULDN'T.