BAE 4100 FLC WERE DIVERTED BY DISPATCHER TO ANOTHER ARPT DURING CRUISE FOR SCHEDULING PURPOSES WITHOUT SUFFICIENT FUEL REMAINING FOR A REQUIRED ALTERNATE.

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ENRTE FROM ORF TO IAD I WAS REROUTED TO RDU BY OUR DISPATCH FOR SCHEDULING REASONS. AFTER TURNING TOWARDS RDU AND COMMITTING MYSELF; I ASKED FOR THE FUEL BURN; MIN FUEL; ETC; FROM DISPATCH. THIS TOOK A WHILE TO FIGURE. MY FO AND I THEN DISCUSSED THE SIT. I THEN WENT BACK TO THE RADIO TO DOUBLE CHK THE WX IN RDU. THERE WASN'T A CLOUD IN SIGHT AT OUR PRESENT POS SO I ASSUMED RDU WOULD BE VFR. MY DISPATCHER CAME BACK; AFTER ANOTHER DELAY; AND TOLD ME THAT RDU HAD 2.5 MI VISIBILITY. I DID NOT HAVE ENOUGH FUEL FOR AN ALTERNATE AT THIS POINT AND RDU WAS MY CLOSEST USABLE ARPT. I FELT I HAD ALREADY COMMITTED MYSELF TOO FAR AND NEEDED TO CONTINUE TO RDU. WE CONTINUED; SHOT THE ILS AND LANDED UNEVENTFULLY. CONTRIBUTING FACTORS INCLUDED THE LACK OF RDU WX IN MY WX PACKAGE SINCE IT WAS NOT OUR ORIGINAL DESTINATION; DELAYS EXPERIENCED IN COMMUNICATING OVER 'ATLANTA RADIO' TO MY DISPATCHER; AFIS SYS BEING UNABLE TO PULL UP WX FORCING ME TO USE A RADIO LINK TO DISPATCH AND FATIGUE. THIS WAS DAY 3 OF A THREE DAY TRIP. THE NIGHT BEFORE I WENT TO SLEEP AT APPROX XA00 AM. AT XF00 AM I WAS WOKEN UP BY SCHEDULING ASKING IF I COULD GO TO THE ARPT TO DEAL WITH A MAINT ISSUE. I DID HAVE MY LEGAL REST AMOUNT BUT NOT MUCH SLEEP. THE FLT WAS A REPO FLT OPERATED UNDER PART 91. I DO NOT KNOW WHAT THE FORECAST AT RDU WAS DURING THIS FLT; ONLY THE CURRENT CONDITIONS.