MLG DEPARTS OVER (MAX GROSS TKOF WT) MAX TKOF GROSS WT.

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MAX ALLOWABLE GROSS WT FOR TKOF IS LOWEST OF: STRUCTURAL; RWY LIMIT; PERFORMANCE LIMIT; AND MAX LNDG WT PLUS FUEL BURNOUT. THIS IS DONE BY COMPUTER AND IN 9 YRS AT MY AIRLINE I HAVE NEVER SEEN IT IN ERROR UNTIL NOW. EARLY AM FLT PLANNING FOR 5 LEGS SHOWED A MAX TKOF GROSS WT OF 105300 LBS (98;000 LNDG WT PLUS 7300 BURNOUT); FOR LEG #3. THE DAY WAS EXTENDED BY MECH DELAYS AFTER A SHORT NIGHT AND WE WERE TIRED. THE FLT PLAN (FROM EARLY AM) SHOWED THE MAX TKOF GROSS OF 105300 LBS BUT THE CURRENT WT MANIFEST AND PERFORMANCE DATA; COMPUTED AND OBTAINED AT/NEAR DEP TIME; SHOWED A MAX TKOF GROSS OF 107100 LBS; (PERFORMANCE LIMITED). WE TOOK OFF AT 106900 LBS AND DISCOVERED THE ERROR ENRTE. WE CONTACTED DISPATCH AND MAINT PLUS THE DECISION WAS MADE TO BURNOFF THE EXCESS FUEL RATHER THAN LAND OVERWT. AN INVESTIGATION IS UNDERWAY. FACTORS: FATIGUE EARLY FLT PLANNING OF MULTIPLE LEGS. DISPATCHER -- LIMITED MAX TKOF GROSS'S NOT CONSIDERED WHEN MORE CURRENT DATA PRESENTED. TOO MUCH TRUST IN COMPUTER PROGRAMMING: WE CHKED 3 OF 4 LIMITING FACTORS. DISCUSSION WITH OTHER PLTS INDICATES THIS IS AN EASY MISS. TRUST IN CURRENT DATA; WHILE IGNORING OLDER DATA. THIS IS USUALLY THE CORRECT THING TO DO.