B727 FLC DISCOVERED A FUEL IMBALANCE AFTER TKOF. AILERON TRIM WAS ASYMMETRICAL.

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ACFT ON GND FOR OVER 1 HR BUT FUELING BEGAN LATE. #1 FUEL QUANTITY GAUGE DEFERRED INOP WHICH REQUIRED FUELER TO DE- FUEL #1 TANK AND FILL WITH KNOWN QUANTITY. FUELER ARRIVED LATE WITH FUEL SLIP TO BE CHKED AND VERIFIED BY FE. MECH PROVIDED DRIPSTICK MEASUREMENTS THAT WERE WELL WITHIN LOAD AND BALANCE TOLERANCES. FE STATED WE HAD THE REQUIRED FUEL FOR BURN AND TAXI ABOARD. PUSH BACK; TAXI NORMAL. AFTER TKOF; I NOTICED IT TOOK 2 1/2 UNITS OF AILERON TRIM FOR LEVEL FLT. WE BEGAN TO INVESTIGATE AND DISCOVERED THE FUEL SHEET SHOWED WE HAD 1800 LBS EXTRA BOARDED. WE ASSUMED THAT THE TRIM SIT WAS CAUSED BY THE FUELER IMPROPERLY LOADING THIS AMOUNT INTO THE #1 TANK (FUEL QUANTITY AND TOTALIZER STILL INOP). LATE FUELING; THE INOP GAUGES; AND A NEWLY DEFERRED FUEL SHUTOFF VALVE IN #1 TANK (JUST BEFORE PUSH BACK); ALL CONTRIBUTED TO A 'RUSHED' PUSH BACK. ALTHOUGH WE HAD MORE THAN THE REQUIRED AMOUNT OF FUEL; WE DID NOT REALIZE THERE WAS AN IMBALANCE. THE MECH'S DRIPSTICK MEASUREMENTS FURTHER ASSURED US THAT NOTHING WAS WRONG. IN THE FUTURE; I WILL DOUBLE-CHK FUEL PAPERS WHEN THERE IS A QUANTITY GAUGE INOP TO HELP INSURE LOAD AND BAL. FLT CONTINUED NORMAL; NORMAL LNDG.