A CL60 CREW; DEPARTING AGC; TURNED 60 DEGS FROM ASSIGNED DIRECT HDG WITHOUT ATC APPROVAL; CITING WX AVOIDANCE THE REASON.

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MYSELF (CAPT) IN R SEAT (PNF). FO IN L SEAT (PF). THE FO WAS A CL60 TYPE RATED PLT WITH APPROX 750 HRS IN CL601 TYPE ACFT; 8500 TOTAL HRS. THE FO WAS ALSO A FILL-IN PLT THAT I HAVE FLOWN WITH BEFORE; BUT NOT IN THE PAST 4 MONTHS. AFTER DEPARTING RWY 28 AT AGC; I CONTACTED PIT DEP CTL; RPTED WE WERE WITH HIM ON THE RWY HDG. HE ACKNOWLEDGED AND TOLD US TO REMAIN AT 3000 FT AND HDG 280 DEGS. AT 3000 FT MSL I COMPLETED THE AFTER TKOF CHKLIST AND NOTICED A TCASII FAIL FLAG. THE PF TOLD ME TO TELL DEP CTL WE WERE DEVIATING TO THE L FOR WX. I LOOKED UP AND SAW HE HAD TURNED THE ACFT TO A HDG OF 220 DEGS. I ASKED DEP CTL IF WE COULD MAINTAIN A HDG OF 220 DEGS FOR WX. HE RESPONDED WE WERE IN 'BIG TROUBLE' AND 'NOT TO WORRY ABOUT THE WX.' HE TOLD US TO TURN R TO A HDG OF 280 DEGS AND THAT HE HAD ARRIVING ACFT TO PIT. HE LATER CAME BACK; GAVE A CLB AND A DIRECT RTE TO A VOR AND A FREQ CHANGE. CONTRIBUTING FACTORS: RAIN; TURB; TCASII FAILURE; AND NOT FLYING WITH THE FO FOR A FEW MONTHS. I SHOULD HAVE BEEN MONITORING THE ACFT WHILE I WAS DOING THE AFTER TKOF CHKLIST AND NOT BEEN PREOCCUPIED WITH THE TCASII FAILURE. THE FO SHOULD HAVE ANNOUNCED THAT HE NEEDED A TURN TO THE L BEFORE OR DURING THE TURN SO I COULD HAVE NOTIFIED DEP CTL SOONER. THE LACK OF COM BTWN THE FO AND MYSELF WAS THE BIGGEST FACTOR IN THIS SIT; IF HE HAD SAID HE NEEDED A TURN TO AVOID WX; I KNOW I WOULD HAVE STOPPED WHAT I WAS DOING (SINCE IT WAS NOT A SAFETY OF FLT ACTION) AND REQUESTED A TURN TO AVOID WX; WHICH WAS A SAFETY OF FLT ACTION.