B737 ACFT WAS DISPATCHED WITH THE CTR FUEL TANK QUANTITY INDICTOR MEL'ED INOP. THE CREW SUSPECTS THEY WERE OVER-FUELED; AND TOOK OFF OVERWT.

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TKOF WAS OVER GROSS WT LIMIT DUE TO MAINT OVER-FUELING ACFT. CTR FUEL GAUGE PLACARDED INOP. MAINT SIGNED FUEL SLIP STATING 21500 LBS TOTAL WITH 1400 LBS IN CTR TANK. CALCULATING FUEL ENRTE; WE DISCOVERED THAT A PROBABLE 3000 LBS MORE FUEL HAD BEEN ADDED THAN DOCUMENTED; THEREFORE CAUSING US TO UNKNOWINGLY TAKE OFF APPROX 2000 LBS OVER GROSS TKOF WT LIMIT. WE BECAME CURIOUS ENRTE WHEN THE CTR FUEL PUMPS TOOK SO LONG BEFORE THE LOW PRESSURE LIGHTS CAME ON. COULD HAVE ALSO BEEN A PROB WITH MAX LNDG WT HAD THE ACTUAL ZERO FUEL WT NOT BEEN LOWER THAN FLT PLAN. I SUSPECTED; DURING THE WAIT FOR THE FUEL SLIP; THAT THE FUELING PROC/SUPERVISION WAS NOT BEING DONE CORRECTLY AS IT TOOK AN EXCEPTIONALLY LONG TIME (20 MINS) FROM END OF FUELING TO RECEIPT OF THE FUEL SLIP. FOR THIS REASON; I QUESTIONED THE MECH IN DETAIL AS TO QUANTITY OF FUEL AND HE REASSURED ME IT WAS CORRECT AS STATED ON FUEL SLIP; 21500 LBS TOTAL; 1400 LBS CTR TANK. I AM GREATLY CONCERNED THIS HAPPENED ALL TOO MANY TIMES AND CAN HAPPEN AGAIN IF THE MECHS SUPERVISING THE ALTERNATE FUELING METHODS ARE NOT MORE ACCURATE.