What was found
AIRCRAFT WAS GROUNDED: PILOT REPORTS APPROXIMATELY 3 MINUTES AFTER AIRBORNE, RH FUEL QTY WAS 500# LESS THAN LH QTY. AFTER 10 MINUTES THE RH QTY WAS 600# LESS AND REMAINED THERE UNTIL LEVEL OFF. THE FMC FUEL QTY ALSO INDICATED 600# LESS THAN TOTALIZER. DID NOT REQUIRE ANY AILERON TRIM ADJUSTMENT AT CRUISE ALTITUDE W / 600# IMBALANCE. SUSPECT RH QTY SENSING ERROR. ADDITIONALLY, ON CLIMBOUT WITH ALL FUEL PUMPS ON, THE RIGHT WING TANK IS DECREASING IN FUEL QUANTITY AT THE SAME RATE AS THE CENTER TANK.THIS IS CAUSING AN INBALANCE OF 800# AT TOP OF CLIMB. AFTER CENTER TANK WAS EMPTY, BALANCED THE WING TANKS. THEY REMAINED IN BALANCE FOR THE DURATION OF THE FLIGHT. ALSO SUSPECT POSSIBLE SLOW FUEL LEAK FUEL WAS 1400# BELOW FLIGHT PLAN AT THE HALF WAY POINT. WINDS AND TEMP ALOFT WERE AS PLANNED FL 370 TAT 27 DEGREES C SAT 53 DEGREES C N1 87.6- 87.7 EGT 661-649 FF 2.56-2.52. MAINTENANCE ACCOMPLISHED FQIS BITE CHECK IAW FIM 28-41-00. NO FAULTS FOUND. SUMPED RIGHT FUEL TANK IAW AMM 12-11-00. MAINTENANCE REMOVED AND REPLACED RT CTR FUEL OVERRIDE PUMP IAW AMM 28-22-21 PUMP, OPS CHECKS GOOD, LEAK CHECKS GOOD. RAN BOTH ENGINES AND VERIFIED THAT FUEL WAS BURNING FROM CTR TANK, NO MIGRATION NOTED.