ACR MLG ACFT ENG FLAME-OUT DURING CLB OUT DUE TO FUEL STARVATION CAUSED BY IMPROPER ACFT FUELING IMBAL.

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SCHEDULED CARRIER TRIP FROM LAX TO DEN. FUEL LOAD FOR 2 PLUS 15 ENRTE TIME WAS 16900 POUNDS PLUS TAXI OF 400 POUNDS. FUEL IN #1 AND 2 TANKS; WING TANKS 8700 POUNDS IN #1 AND 8700 POUNDS IN #2. THE ACFT OVER NIGHT AT LAX. THE FUELER MENTIONED THAT THE ACFT HAD AN ABNORMAL FUEL LOAD PRIOR TO HIS REFUELING FOR THE FLT. I DID NOT PICK UP ON THE AMOUNT IN THE TANKS BEFORE REFUELING. HE STATED THAT THE FUEL WAS BALANCED BEFORE REFUELING. THE BALANCING WAS DONE BY A STATION MAINT AND THE ACFT WAS FUELED FOR THE FLT TO DEN; 8700 POUNDS IN TANKS 1 AND 2. THIS CONVERSATION TOOK PLACE IN THE COCKPIT AND I TESTED THE GAUGES; THE TEST WAS NORMAL SHOWING PROPERLY FUNCTIONING GAUGES. THE TKOF ROLL WAS NORMAL; AFTER LIFT OFF THE ACFT WAS VERY L WING HVY. THE LAX 1 DEP WAS DOWN AND SOMEWHERE BTWN LIFT OFF AND ABOUT 2000 FT BOTH FORWARD AND AFT LOW PRESSURE BOOST PUMPS LIGHT CAME ON THEN WENT OFF. WE WERE VERY BUSY WITH THE DEP AND TRYING TO DETERMINE WHY THE ACFT WAS SO L WING HVY. I THOUGHT THAT PERHAPS THE AILERON TRIM HAS MALFUNCTIONED AND ASK THE FO TO GO BACK AND CHK THE TRIM. WE HAD CLBED THROUGH 1000 FT. HE HAD JUST STARTED TO GO BACK WHEN THE #2 ENG FLAMED OUT. DURING THE CLB I TESTED THE FUEL GAUGES 2 OR 3 TIMES EACH TEST SHOWED NORMAL GAUGE OP. WHEN THE #2 ENG QUIT THERE WAS NO LONGER ANY DOUBT ABOUT OUR PROBLEM; NO FUEL IN #2 TANK AND ABOUT 7500 POUNDS IN #1 TANK. I OPENED THE FUEL XFEED; PULLED THE #2 THROTTLE TO IDLE AND SELECTED FLT START ON THE IGNITION. THE ENG HAD SPOOLED DOWN TO ABOUT 70 PERCENT N2 THEN RESTARTED. LA CTR WAS INFORMED OF OUR SITUATION AND WE RETURNED TO LAX. AFTER LNDG THE #2 TANK SHOWED 60 POUNDS FUEL AND A TEST OF THE FUEL GAUGES SHOWED THAT #2 GAUGE HAD 2 ERROR CODES. THERE WAS A LONG HISTORY; ABOUT A WEEKS WORTH OF PROBLEMS WITH THE #2 GAUGE. I DID NOT CHK THE MAINT HISTORY BEFORE THE FLT. THE GAUGE HAD BEEN REPAIRED ON THE X OF MAY AND THE ACFT HAD FLOWN; TROUBLE-FREE FOR ABOUT 14 HRS.