DELAYS; BAD WEATHER AT DESTINATION AND AN EXTENDED LONG DUTY DAY CAUSE B737-300 FO TO REFUSE LAST LEG DUE TO FATIGUE.

Narrative

I WAS ON THE SECOND TRIP OF BACK-TO-BACK IDENTICAL SCHEDULES. I HAD A HARD TIME SLEEPING ON THE FIRST TRIP AT THE HOTEL SINCE THE ROOM WAS VERY COLD; BUT DIDN'T DEEM IT SERIOUS ENOUGH TO WRITE UP IN A RPT. ON THE SECOND TRIP; WE WERE ADVISED THAT OUR DEP TIME OUT OF ZZZ WOULD BE OVER 2 HRS LATER. THE FLT ATTENDANTS GOING TO MY FINAL DEST WERE WITH ME IN ZZZ AND I KNEW IT WOULD BE IMPOSSIBLE TO LEAVE ZZZ2 AT THE POSTED DEP TIME. I DID THE MATH AND CONCLUDED WE WOULD LIKELY ARRIVE IN ZZZ2 WELL AFTER XA00; AND THE FORECASTED WX INCLUDED VISIBILITY OF 1 MI IN BR; AND TEMPORARY SN WITH LOWER VISIBILITY. I WOULD ALSO BE CHANGING TO A NEW CAPT IN ZZZ2. I WAS ALREADY FEELING QUITE DRAINED FROM THE LONG UNFORESEEN SIT IN ZZZ; AND FLYING INTO POTENTIAL WX AT XA00 AFTER BEING UP FOR 19 HRS DID NOT SEEM PRUDENT OR PROFESSIONAL. THEREFORE; I CALLED IN FATIGUED WITH THE CREW DESK TO GIVE THEM AS MUCH TIME AS POSSIBLE TO RE-CREW THE FLT. THE CREW DESK REQUESTED THAT I DEADHEAD AND FLY THE RETURN FLT HOME THE NEXT DAY AND I AGREED.