B737 HAS STICKY FUEL GAUGE WHICH READ LOW. PROB TREATED AS A FAULTY GAUGE. EVENTUALLY; ENOUGH FUEL WAS BURNED FROM THE TANK TO CAUSE LOW PRESSURE LIGHTS TO COME ON. THE TANK WAS NOT DRIPSTICKED UNTIL AFTER COMPLETION OF THE SECOND LEG.

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APPROX 45-60 MINS AFTER DEP FROM JFK; I NOTICED A FUEL IMBAL OF 3000 LBS OF FUEL BTWN THE L AND R MAIN FUEL QUANTITY GAUGES. THE L MAIN FUEL QUANTITY GAUGE READING THE LOWER FUEL. ALL SYS WERE NORMAL PRIOR AND NO XFEED WAS PERFORMED. I THEREFORE TESTED THE FUEL QUANTITY; AND THEN POPPED AND RESET THE FUEL QUANTITY CIRCUIT BREAKER. THE L FUEL GAUGE STILL SHOWED A LARGE IMBAL. THEN; TURNED THE AUTOPLT OFF AND TESTED THE FEEL OF THE ACFT. THE ACFT FELT OF EQUAL BAL. UPON ARR AT GSP; I LOOKED AT THE FUELING PANEL UNDER THE ACFT WING AND CHKED FOR FUEL LEAKS AROUND THE L WING. THE #1 TANK FUEL GAUGE REPEATED THE COCKPIT GAUGE IMBAL. IN GSP; I PHONED MAINT CTL. WE BOTH AGREED I WOULD CONTINUE THE FLT TO CAE AND FURTHER MONITOR THE FUEL GAUGE. AFTER TKOF FROM GSP; JUST PRIOR TO LEVELOFF I OBSERVED A L MAIN FORWARD LOW PRESSURE LIGHT. PROCS CALL FOR FUEL XFEED OPEN; ALL MAIN FUEL TANKS ON. I FOLLOWED THAT PROC. UPON ARR AT CAE; MAINT DRIPSTICKED THE L MAIN AND FOUND I HAD AN IMBAL DUE TO LOW FUEL IN THE L MAIN AND AT THAT TIME DMI THE L FUEL QUANTITY GAUGE AS UNRELIABLE. I CONTINUED THE FLT TO ATL. I FOUND THE L FUEL QUANTITY GAUGE TO STICK. I ALSO OPENED THE FUEL XFEED AND WITH ALL MAIN TANKS ON; FOUND THAT BOTH ENGS FED FROM THE L MAIN TANK. SUPPLEMENTAL INFO FROM ACN 367583: SEE ATTACHED LETTER OF INFO TO CHIEF PLT. CRM WAS NOT ADHERED TO NOR WAS IT EVEN CONSIDERED BY THE CAPT. NOT THE WAY I WANT TO BE TREATED AS A FELLOW CREW MEMBER.