A B737-300 WAS DISPATCHED IN NON COMPLIANCE WITH A FUEL IMBAL REQUIRING OUT OF LIMITS AILERON TRIM. SPECIAL FUELING PROCS WITH INOP FUEL QUANTITY INDICATOR WERE NOT FOLLOWED PER THE MEL.

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ACFT WAS WRITTEN UP AS HAVING AN INOP #2 FUEL GAUGE; SO WE FOLLOWED THE INOP FUEL GAUGE INOP FUELING PROC. WE NOTICED THAT THE INBOUND CREW HAD ENTERED AN ON-BLOCK FUEL AMOUNT OF 10700 LBS. THIS CONFLICTED WITH THE 'STICK' VALUE OF THE FUEL; WHICH TRANSLATED TO A TOTAL OF 8200 LBS; A 2500 LB DISCREPANCY. ALTHOUGH APU WAS RUNNING; THE FLT WAS A 'THROUGH' AND ACFT HAD NOT BEEN SITTING VERY LONG. I NOTICED THAT THE 3 FUELERS WERE HAVING A DISCUSSION AROUND THE TRUCK REGARDING THE FUELING; SO I WAS PARTICULARLY CAREFUL IN REVIEWING THE PAPERWORK AND ASKED MANY QUESTIONS ABOUT IT. THE POST FUELING STICK VALUE WAS 16.7 INCHES; WHICH TRANSLATED TO 5600 LBS IN THE #2 TANK WITH 5600 LBS INDICATED ON THE FUELING GAUGE FOR THE #1 TANK. 444 GALLONS WERE ADDED TO BRING THE TOTAL FUEL TO 11200 LBS (CLR + TAXI). FO AND I WERE SATISFIED. ON TKOF; ACFT REQUIRED A LARGE AMOUNT OF R AILERON AND TRIMMED UP WITH A FEW UNITS OF L TRIM ON THE INDICATOR. LNDG REQUIRED SOME L AILERON AS WELL. I HAD THE SAME AIRPLANE FOR THE FLT THE NEXT MORNING BACK TO ZZZ1. IN CHKING THE PAPERWORK; I FOUND THAT THERE WAS A 2000+ LB DISCREPANCY BTWN THE WING TANKS. TALKED TO MAINT AND THEY RECOMMENDED THAT THE FUEL BE METERED FROM THE R MAIN TO THE L MAIN.