FLC OF AN LTT USED RWY OF INSUFFICIENT LENGTH FOR THE ACFT MAX TKOF WT DUE TO A PORTION OF THE USABLE RWY BEING CLOSED.

Narrative

WE LANDED AT ROC ON RWY 28 BECAUSE RWY 4/22 WAS CLOSED AS PER ATIS. WE WERE RUNNING LATE AND HAD ONLY 15 MINS TO TURN AROUND. I RECEIVED THE WX PACKAGE AND STARTED TO LOOK FOR THE DEST WX IN ORDER TO COME UP WITH A FUEL LOAD. THAT IS WHEN OPS SAYS YOU GUYS ARE GOING TO BE FULL OUT OF HERE. I GAVE THEM A FUEL LOAD AND WENT INSIDE TO USE THE BATHROOM. ON THE WAY OUT I PICKED UP A SNACK. AFTER I FINISHED MY LAST BITE THE FUELER SHOWS UP AND THE PAX ARE BOARDING. I HAVE TO BE BY THE DOOR DURING REFUELING. I AM THINKING ABOUT WT LIMITS FOR RWY 28. I STILL ASSUMED THAT RWY 22 WAS CLOSED AND WE MIGHT HAVE TO BUMP OFF SOME PAX. I HAD TO HURRY WITH THE TOTAL WT TO COME UP WITH THE PLAN. MY FO SAYS WE NEED RWY 22 AND IT'S OPENED. THAT'S WHAT I NEEDED TO HEAR. I DID NOT LOOK AT THE NOTAM NOR DID MY FO LISTEN TO ATIS COMPLETELY. WE TOOK OFF ON RWY 22 WITH THE LAST 1655 FT CLOSED. IF THE TWR WOULD HAVE SAID; 'TAXI TO RWY 22 THE LAST 1655 FT ARE CLOSED.' I WOULD HAVE NEVER USED IT. DULLES ALWAYS TELLS US ABOUT RWY CHANGES EVEN THOUGH IT IS ON THE ATIS AND NOTAMED OUT.