B757 FLC ENCOUNTERED ENRTE WX; REQUIRING EASTERLY DEV. ARTCC CTLR ISSUED HDGS THAT WOULD CAUSE WX ENCOUNTER. CTLR ASKED IF PIC WAS REFUSING CLRNC AND PIC AFFIRMED. WHEN WX WAS NOT A FACTOR; PIC ADVISED THEY COULD RESUME NBOUND HDG AND WAS SO CLRED. PIC CONCERNED WITH PERCEIVED CTLR ATTITUDE.

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ENRTE FROM MCO TO DTW; WE ENCOUNTERED TSTMS OVER THE TLH AND AMG AREA. WE WERE FLYING AT FL240 DUE TO THE TURB RPTED AT THE HIGHER ALTS. WE ASKED AND RECEIVED CLRNC TO DEVIATE TO THE E OF COURSE AND TURNED TO A 030 DEG HDG. AFTER A FEW MINS; ZJX REQUESTED WE TURN TO A 350 DEG HDG (BACK TOWARDS THE WX). WE REPLIED THAT WE COULD ONLY TURN TO A 010 DEG HDG AND TURNED TO THAT HDG. AFTER 1 MIN; JAX STATED THAT OTHER ACFT HAD FLOWN THROUGH THAT AREA AND NOW DIRECTED US TO TURN TO A 330 DEG HDG. AGAIN; WE STATED THAT WE WERE UNABLE TO MAKE THE TURN DUE TO WX. JAX SAID THAT WAS UNACCEPTABLE AND TO TURN TO 330 DEGS. WE THEN SAID THAT WE COULD MAYBE TURN TO 350 DEGS; BUT THAT WAS ALL FOR NOW. JAX SAID THAT WAS UNACCEPTABLE AND TO TURN TO 330 DEGS. THE CAPT CAME ON THE RADIO AND STATED THAT WE WERE TURNING TO 350 DEGS AND COULD NOT TURN FURTHER DUE TO WX. HE ALSO TOLD JAX THAT IF THERE WERE A TFC CONFLICT; WE WOULD CLB OR DSND AS CTR NEEDED. JAX CAME BACK ASKING IF WE WERE REFUSING THE CLRNC. THE CAPT STATED THAT WE WERE AT THIS TIME. A FEW MINS LATER WHEN IT WAS SAFE; WE ADVISED ZJX THAT WE COULD TURN TO 330 DEGS AND TURNED TO 330 DEGS. ZJX NEVER DID INDICATE IF THERE WAS A TFC CONFLICT. ATC HAS TO REALIZE THAT WE WILL NOT ACCEPT A CLRNC THAT PUTS THE SAFETY OF THE ACFT AT RISK.