FLT CREW DEP FROM FXE AT 7000 FT IS QUESTIONED BY CTLR REGARDING WX DEV REQUEST.

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I DEPARTED FT LAUDERDALE EXECUTIVE ARPT; FXE; RWY 8; AT XA16 LCL TIME. I TURNED TO THE ASSIGNED HDG AND ALT OF 330 DEGS AND 2000 FT. MY COPLT RPTED INTO MIA DEP ON 119.7 WHO TOLD US TO CLB TO 3000 FT ON THE 330 DEG HDG. THE CTLR THEN HANDED US OFF TO MIA CTLR ON 126.05. THE NEW CTLR TOLD US TO TURN TO 270 DEGS AND CLB TO 16000 FT. MY COPLT; AT MY DIRECTION; TOLD THE CTLR WE NEEDED TO TURN R; (NE); FOR WX. THE CTLR CAME BACK ON AND SAID; 'NO; I AM NOT PAINTING ANY WX; FLY 270 DEGS.' AT THAT TIME; BECAUSE WE WERE JUST A MOMENT FROM ENTERING WHAT MY COPLT AND I PERCEIVED AS HAZARDOUS WX; I BROKE IN ON THE CONVERSATION AND TOLD THE CTLR 'I DON'T CARE IF YOU ARE PAINTING WX OR NOT. I HAVE A LARGE BUILDUP IN FRONT OF ME AND I AM TURNING TO AVOID IT.' THE CTLR THEN SAID OK; I WILL MAKE A NOTE FOR THE RECORD. I STOPPED THE CLB AND TURNED NE TO TRY AND GO SOMEWHAT UNDER AND AROUND THE BUILDUP. IT WAS TOO LATE BY THEN AND WE WERE TOSSED ABOUT BRIEFLY AS WE SKIRTED THE WX. POPPING OUT THE BACKSIDE OF IT; I RESUMED THE ASSIGNED CLB TO 16000 FT. THE CTLR CAME BACK ON AND ASKED IF WE COULD TURN TO A HDG OF 120 DEGS; A COMPLETE COURSE REVERSAL. I ANSWERED THAT YES WE WERE PAST THE WX AND WOULD BE GLAD TO TURN WHEREVER SHE WOULD LIKE. WE WERE GIVEN ANOTHER R TURNED BACK TO THE ORIGINAL HDG OF 330 DEGS; MAKING A TOTAL 360 DEG TURN. THESE EVENTS HAPPENED VERY RAPIDLY RIGHT AFTER TKOF WITH VERY LITTLE TIME LEFT TO CONVERSE AND MANEUVER. I DON'T UNDERSTAND WHY THE CTLR EVEN MADE THE COMMENT THAT SHE WAS NOT PAINTING ANY WX. IT WAS IRRELEVANT. SHE WASN'T THERE. SHE MAY VERY WELL HAVE NOT BEEN PAINTING ANY WX AS THERE PROBABLY WASN'T ENOUGH WATER IN THE BUILDUP TO PAINT BUT IT WAS VERY REAL TO US. I WOULD HAVE GLADLY ACCEPTED ANY HDG TO HELP HER TFC CTL SIT AS LONG AS IT WAS AWAY FROM THE WX. THE CTLR OFFERED NO HELP IN THAT REGARD. SO I SIMPLY TURNED TO WHAT I SAW AS THE BEST COURSE OF ACTION AT THE TIME.