A DISPATCHER CHANGED DEST OF A B737 FLT DUE TO WX; WHICH CAUSED SERIOUS FUEL ISSUES AS THE RESERVES WERE BEING COMPROMISED.

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ZZZ FORECAST WAS VMC ALL DAY. I DISPATCHED FLT NUMBER WITH 30 MINS OF CONTINGENCY FUEL. AN AMENDED FORECAST FOR ZZZ CAME OUT WITH TSTMS IN THE FORECAST. AT THAT TIME; I CHKED THE AREA RADAR. THERE WASN'T ANYTHING DEVELOPING AROUND ZZZ AT THE TIME. THE ONLY WX WAS ABOUT 70 TO 80 MI S AND THE CONVECTIVE SIGMET SHOWED MOVEMENT FROM 140/20. I THEN CHKED MY MONITOR TO SEE WHAT I HAD TO ZZZ AND SAW FLT NUMBER HAD ALREADY PUSHED OFF THE GATE. AFTER DEP; I NOTICED A SINGLE CELL DEVELOPING ABOUT 10 MI S OF THE FIELD. WHEN FLT NUMBER WAS ABOUT 30 MIN FROM ZZZ I CALLED TO UPDATE THE CREW ON THE WX. AT THAT TIME ZZZ WAS STILL VMC AND THE CELL WAS STILL ABOUT 8 MI S AND MOVING VERY SLOWLY TO THE N. I MONITORED THE DISPATCH RADIO; ZZZ STATION RADIO; AND FLT TRACKING SYS. I NOTICED FLT NUMBER HAD DROPPED OFF FLT TRACKING SYS SO I TURNED BOTH RADIO STATIONS OFF. THE CELL WAS STILL 2 TO 3 MI S OF THE FIELD. ABOUT 5 MINS LATER SOMEONE SAID 3 FLTS HAD MISSED IN ZZZ. I CALLED ZZZ OPS TO CHECK ON FLT NUMBER AND THEY SAID HE DIDN'T MAKE IT IN. AT THAT TIME; I PULLED BOTH RADIOS BACK UP AND STARTED PLANNING THE BURN TO YYY. I HEARD FLT NUMBER CALLING ON THE DISPATCH RADIO. CAPT SAID THEY HAD 7.4 OR 7.5 ON THE GAS. I TOLD CAPT TO STAND BY; THE COMPUTER WAS STILL PLANNING THE BURN TO YYY. WHEN THE BURN CAME UP; I TRIED TO CALL FLT NUMBER ON THE DISPATCH RADIO. THE DISPATCH RADIO KEPT KICKING OFF LINE. I TRIED NUMEROUS TIMES ON THE DISPATCH RADIO AND THE ZZZ STATION RADIO. FINALLY THE CAPT CALLED ZZZ STATION TRYING TO REACH DISPATCH AND THE ZZZ OPS AGENT WORKING THE RADIO TOLD HIM I HAD BEEN TRYING TO REACH HIM. I TOLD CAPT THE BURN TO YYY WAS 2.9 AND HE INFORMED ME THAT HE HAD EITHER 6.4 OR 6.5 ONBOARD. I IMMEDIATELY TOLD THE CAPT TO DIVERT TO YYY AND GAVE TIME AND INITIAL. AFTER FLT NUMBER HAD STARTED TOWARD YYY; I REALIZED THAT WE WOULD BURN INTO THE FAR FUEL.