ACR ON DEP IS GIVEN VECTORS FOR AVOIDANCE OF TFC.

Narrative

ON DEP FROM ZZZ RWY 10; WE REQUESTED 120 DEG HDG TO AVOID TSTMS OFF DEP END AND TO N. A C172 HAD JUST DONE A TOUCH-AND-GO AND APPEARED TO BE DEPARTING IN THE SAME DIRECTION. ON OUR FIRST CALL TO DEP CTL; WE WERE INSTRUCTED TO JOIN ZZZ2 (AS FILED). WE REPLIED THAT WE COULDN'T DUE TO TSTMS. DEP CTL NEVER ACKNOWLEDGED OUR RPT. AT THE TIME OF THIS CLRNC; WE WERE PASSING THE 075 DEG RADIAL OFF LAN VOR. I INSTRUCTED THE FO (PF) TO BEGIN A L TURN TO JOIN AND AGAIN TRIED TO INFORM DEP OF THE WX PROB. DEP THEN ISSUED TFC ALERTS AND HDGS TO SEPARATE US FROM THE C172. WE SAW THE C172 ON TCASII BUT NEVER RECEIVED AN ADVISORY. WE ALSO HAD THE C172 VISUALLY AND RPTED SAME; BUT BECAUSE DEP WAS RAPIDLY GIVING OUT HDGS; I DON'T THINK THEY HEARD OUR RPT. THIS COULD ALL HAVE BEEN AVOIDED IF TWR HAD DELAYED OUR DEP A LITTLE LONGER OR IF DEP CTL WOULD HAVE ACKNOWLEDGED OUR FIRST REPLY THAT V133 WAS NOT USABLE DUE TO WX. AS IT WAS; WE WERE IN MODERATE TURB SKIRTING THE WX UNTIL ADEQUATE SEPARATION WAS OBTAINED AND WE WERE ALLOWED TO FLY CLR OF THE WX.