B737-700 CREW DEVIATING AROUND WX WAS REQUIRED TO DECLARE AN EMER TO AVOID BEING VECTORED INTO A TSTM.

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LOTS OF SEVERE WX FROM S FLORIDA TO THE CAROLINAS. WE WERE DEVIATING AROUND VERY LARGE TSTMS AND WERE R OF INTENDED COURSE DUE TO WX DEVS. THE ZJX CTLR CLRED US DIRECT TO MILLE INTXN; DIRECT CHS. PRIOR TO REACHING MILLE; THE CTLR SAID WE WERE APCHING A WARNING AREA AND ISSUED A VECTOR THAT WOULD HAVE PUT US IN A VERY LARGE TSTM. WE ADVISED THE CTLR THAT WE WERE UNABLE TO ACCEPT THAT TURN DUE TO WX. HE THEN SAID; 'EXERCISING YOUR EMER AUTH; SQUAWK 7700 AND CONTINUE YOUR PRESENT COURSE.' WHEN CLR OF THE TSTM. WE ADVISED THE CTLR AND HE ISSUED US AN INTERSECTING VECTOR TO REJOIN THE AIRWAY AND WHEN OUT OF THE WARNING AREA; HE REISSUED US OUR ORIGINAL XPONDER CODE. SUPPLEMENTAL INFO FROM ACN 622895: MANY MINS LATER WHEN WE WERE ABEAM MILLE WE WERE TOLD TO FLY A 010 DEG HDG; WE TOLD ATC 'UNABLE DUE TO WX.' A CELL WAS RIGHT OVER MILLE WITH AN OVERHANG EXTENDING ABOUT 10 M I TO THE E. THE CELL WAS LARGE; PAINTING WELL AND I WOULD EXPECT ATC TO EASILY SEE THE SAME. THE FOLLOWING IS THE EXACT CONVERSATION: ATC: 'COMPANY NUMBER; FLY HDG 010 DEGS.' COMPANY: 'UNABLE DUE TO WX.' ATC: 'SQUAWK 7700; EXERCISE EMER AUTH; I WILL PROVIDE TA'S.'