AN FK100 FLC RESPONDS TO A SECOND GPWS ALERT AT 11000 FT WHILE DEVIATING IMC AROUND TSTM ACTIVITY NEAR YRK; KY.

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AFTER BEING DELAYED ON GND FOR 3 HRS IN ORD; WE WERE ALLOWED TO DEPART TO DCA ON A MORE DIRECT ROUTING. DISPATCH SENT MESSAGE TELLING US WE WERE GOING TO BE 3000 LBS OVERWT. I ELECTED TO GO LOW TO INCREASE FUEL BURN AND WE HAD TO GO AS FAR S AS IIU TO GET AROUND WX. WHEN WE STARTED TO PICK OUR WAY THROUGH THE WX; WE GOT A GPWS WARNING OF TOO LOW TERRAIN. WE DOUBTED THE WARNING KNOWING OUR HIGHEST EMER SAFE ALT WAS APPROX 3000 FT IN THE AREA. WE RECEIVED ALMOST IMMEDIATELY A SECOND GPWS LEARNING OF TOO LOW TERRAIN AND I PERFORMED THE ESCAPE MANEUVER. WE ADVISED ATC OF THE CLB AND THEY TOLD US THERE WAS NO CONFLICTS. WE CLBED TO 12000 FT AND WAS SUBSEQUENTLY CLRED BY ATC TO CLB TO 15000 FT. ATC INFORMED US THAT THERE WAS NO LOSS OF SEPARATION. EVEN THOUGH WE KNEW TERRAIN WAS NOT A FACTOR; I THOUGHT IT PRUDENT TO CLB BEING IN MODERATE PRECIPITATION AND A SECOND WARNING SOUNDED. SUPPLEMENTAL INFO FROM ACN 514693: WHILE PICKING OUR WAY THROUGH TSTMS; WE GOT A GPWS WARNING OF TOO LOW TERRAIN. WE WERE IFR AT THE TIME AND HAD NO VISUAL TERRAIN CLRNC.