B757 FLT CREW RESPOND TO TCASII RA WHEN DIVERTING AROUND WX ON DEP FROM MCO. DELAY IN CLB CLRNC DUE TO WX; CLRNC VERIFICATION AND NORDO ACFT CONTRIBUTE TO EVENT ACTIONS BY FLT CREW AND ATC.

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STRAIGHT AND LEVEL AT 14000 FT NBOUND; DIRECT TO GUANO INTXN ON MCCOY 9; REQUESTED A 30 DEG R TURN TO AVOID DOPPLER RETURNS AND DARK CLOUDS AHEAD. CTLR REQUESTED STAY ON COURSE WHILE HE COORD WITH CTR. 10 MI FROM WX; CTLR REPLIED; 'UNABLE DUE TO TFC.' ALSO; HE NOTED PREVIOUS ACFT HAD RPTED ONLY LIGHT CHOP GOING THROUGH. WE ELECTED TO STAY ON COURSE; ASKED FOR 10 DEGS R WHICH WAS APPROVED. SHORT TIME LATER; ATC DIRECTED R TURN TO 090 DEGS FROM 360 DEG HDG FOR TFC. I BEGAN R TURN TO 090 DEG HDG ON AUTOPLT. OBSERVED ACFT IN LEVEL TURN. AT THIS POINT; THERE WAS ATC COMMENTARY ABOUT A NORDO ACFT AND I HEARD MENTION OF '230' AND THOUGHT IT HDG ASSIGNMENT FOR ANOTHER ACFT. I HEARD NO CALL SIGN ASSOCIATED WITH THE '230' CLRNC.' I SAW THAT THE FO HAD SET '230' IN THE ALT WINDOW. I REQUESTED HE CONFIRM WITH ATC. CTLR REPLIED; 'WHEN ARE YOU GOING TO START YOUR CLB?' I IMMEDIATELY MANUALLY ADVANCED THE THROTTLES; DISCONNECTED AUTOPLT AND PITCHED ACFT UP. TCASII RA TO DSND SOUNDED; BUT ACFT WAS ALREADY WELL INTO AN AGGRESSIVE CLB; SO I STAYED WITH THE CLB. TCASII QUICKLY CHANGED TO 'CLB NOW' RA. WE QUICKLY GAINED ALT SEPARATION ON A NEW HDG. FO RPTED PASSING 15500 FT AND WE SAW 1200 FT SEPARATION ON TCASII DISPLAY ABOVE TFC. ATC THEN CLRED US TO 300 DEG HDG; ZJX FREQ; ON COURSE. OUR ESTIMATE FOR ELAPSED TIME FROM REFUSED WX DEV TO TCASII RA WAS AROUND 90 SECONDS. SUPPLEMENTAL INFO FROM ACN 609218: ATC DIRECTED TURN TO 090 DEGS FROM THEN 360 DEG HDG. CAPT INITIATED TURN. ATC SAID TURN WAS FOR TFC CO-ALT AND NORDO AND DIRECTED CLB TO FL230. I READ BACK AND SET '230' IN WINDOW. I WAS TRYING TO FIND TFC ON TCASII DISPLAY AND WE WERE IMC. AT SOME POINT THE CAPT ASKED ME TO CONFIRM FL230 ALT ASSIGNED AND I CALLED ATC. HIS VERBIAGE MADE CLR HE WANTED AN IMMEDIATE EXPEDITED CLB TO FL230. NEARLY SIMULTANEOUSLY; WE RECEIVED A TCASII RA AND RED TFC DISPLAY AND DSND COMMAND. THE CAPT CONTINUED CLB. HAD HE NOT; I WOULD HAVE STRENUOUSLY OBJECTED; AS WE WERE COMMITTED AGGRESSIVELY TO CLBING. ALL OF THIS TOOK PLACE IN IMC AND IN MY OPINION A VERY SHORT TIME SPAN.