WDB LANDS OVERWEIGHT DUE TO FAULTY WEIGHT AND BALANCE DOCUMENTATION. ALPHA WARNING ALERTS FLT CREW TO ERROR.

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AFTER TKOF WE WERE GIVEN A HDG TO JOIN A RADIAL. I ATTEMPTED TO ARM NAV MODE BUT THE SYS WOULD NOT ARM. THE TYPE OF NAV SYS INSTALLED IN SOME OF OUR ACFT WILL NOT ALLOW YOU TO MANUALLY TRACK A RADIAL AND YOU MUST HAVE THE ABILITY TO PROGRAM THE FMC AND ENGAGE NAV MODE. THIS PARTICULAR ACFT HAD THAT TYPE OF NAV SYS INSTALLED; SO WE MANUALLY TURNED ON COURSE. IN ADDITION TO THE INABILITY OF THE NAV SYS TO ARM; MY COMPASS WAS NOW INTERMITTENTLY INOP. I ATTEMPTED TO ARM NAV MODE NUMEROUS TIMES WITH NO SUCCESS. ABOUT THIS TIME ATC ASKED US WHAT OUR HDG WAS. I GAVE THEM OUR HDG AND INFORMED THEM OF OUR SITUATION AND ASKED FOR RADAR VECTORS UNTIL WE COULD SORT OUT OUR PROB. ATC GAVE US A TURN AND ASKED US IF WE WANTED TO RETURN TO THE ARPT; BUT I TOLD THEM WE WOULD LIKE RADAR VECTORS TO CONTACT OUR COMPANY AND WORK THROUGH OUR NAV PROB. WE INITIATED A PHONE PATCH WITH THE COMPANY MAINT DEPT TO DISCUSS OUR PROBS AND SEE IF THEY COULD OFFER ANY SUGGESTIONS THAT WOULD RESOLVE OUR ISSUES. INITIALLY MAINT WANTED US TO CONTINUE TO ZZZ BUT; GIVEN THE STATE OF OUR NAV SYS; I WAS NOT COMFORTABLE WITH THIS AND SUGGESTED ZZZ1 AS A SUITABLE LOCATION. ZZZ AND ZZZ1 ARE BOTH MAINT BASES FOR THE COMPANY. MAINT SAID THEY WOULD RESEARCH THE PROBS AND CALL US BACK. ATC WAS CONTINUING TO GIVE US RADAR VECTORS AND QUERIED US AGAIN ABOUT RETURNING TO OUR DEP ARPT. I ADVISED THEM THAT IF WE RETURN TO OUR DEP ARPT WE WOULD BE REQUIRED TO DUMP FUEL; AND DID THEY HAVE AN AREA WE COULD USE? THEY INFORMED ME THAT THEY DID NOT HAVE A SPECIFIC FUEL DUMP AREA DESIGNATED FOR THIS PURPOSE. SOMETIME LATER; WE RECEIVED A CALL FROM THE COMPANY AND IT WAS DETERMINED THAT WE WOULD CONTINUE TO ZZZ1. WHILE WE WERE ENRTE TO ZZZ1; I ASKED OUR FE WHAT THE ACFT MAX LNDG WT WAS. WE HAVE DIFFERENT LNDG WTS FOR DIFFERENT CONFIGNS OF OUR VARIOUS ACFT. HE INFORMED ME OUR ACFT LNDG WT WAS 436000 LBS AND THAT WE WOULD BE LNDG AT 412000 LBS. I INFORMED ATC OF OUR DESIGN TO CONTINUE TO ZZZ1; BUT WE COULD ONLY USE CONVENTIONAL VOR NAV. THEY ISSUED US HDGS UNTIL WE COULD PROCEED DIRECT FROM ONE VOR TO THE NEXT. UPON OUR ARR INTO THE ZZZ1 AREA; WE WERE GIVEN AN ARR PROC WHICH ALLOWED US TO USE OUR VOR FOR THE APCH. WE ACCEPTED THIS ARR AND FLEW THE APCH AS CONSTRUCTED. AS WE WERE APCHING 10000 FT AND 250 KTS; WE RECEIVED AN ALPHA SPD DISPLAY. I ASKED OUR FE TO CHK OUR WT AND SPDS TO BE SURE THEY WERE CORRECT; BECAUSE WE SHOULD NOT HAVE HAD AN ALPHA SPD DISPLAYED AT THIS TIME. HE SAID HE CHKED THE WT AND SPDS AND THEY WERE CORRECT. I ASKED ATC IF WE COULD FLY AT A HIGHER AIRSPD AND THEY APPROVED MY REQUEST FOR AS LONG AS THEY COULD AND WHEN I HAD TO SLOW DOWN; WE CONFIGURED THE ACFT. AS WE WERE SLOWING DOWN TO OUR NEXT BUG SETTING; I AGAIN SAID 'THIS DOES NOT LOOK RIGHT; WHY ARE WE GETTING ALPHA SPD?' I ASKED HIM AGAIN TO RECHK THE WT AND SPDS. HE SAID THE WT AND SPDS WERE CORRECT AND HE DID NOT KNOW WHY WE WERE GETTING ALPHA SPD. MY SOLUTION WAS TO BUMP THE AIRSPD UNTIL ALPHA WAS NO LONGER DISPLAYED. AT NO TIME WAS THE ACFT SLOWED DOWN BELOW ALPHA SPD. THE SPD BUG WAS BROUGHT DOWN TO A POINT THAT WOULD NOT DISPLAY ALPHA SPD AND WE FLEW THAT AIRSPD. THE REMAINDER OF THE ARR INTO ZZZ1 WAS UNEVENTFUL AND WE LANDED THE ACFT NORMALLY. MAINT REPAIRED THE ACFT AND WE DEPARTED ONCE AGAIN TO OUR ORIGINAL DEST WITHOUT FURTHER ISSUES. ABOUT 14 HRS AFTER WE ARRIVED INTO ZZZ2; WHILE I WAS IN CREW REST; I RECEIVED A PHONE CALL FROM OUR COMPANY ABOUT A POSSIBLE OVERWT LNDG IN ZZZ1. I TOLD THEM I DIDN'T BELIEVE THAT WAS CORRECT; BECAUSE WE CHKED OUR MAX LNDG WT AND WE WERE WELL BELOW THAT. THEY READ ME THE WT AND BAL NUMBERS AND I REALIZED THAT IN FACT WE HAD LANDED OVERWT. THE ACFT HAD ALREADY DEPARTED TO ANOTHER LOCATION AND WAS CURRENTLY ENRTE BACK TO ZZZ2 AND UPON ITS ARR IT WOULD UNDERGO AN OVERWT LNDG INSPECTION. THE OVERWT LNDG INSPECTION DID NOT REVEAL ANY DISCREPANCY WITH THE ACFT AND THE ACFT DEPARTED APPROX 2 HRS LATE. SHOULD I HAVE KNOWN THE ACFT WAS OVERWT AND THAT WAS WHY WE WERE GETTING ALPHA SPD; YES I SHOULD HAVE. SHOULD I HAVE SEPARATELY LOOKED AT THE ZERO FUEL WT AND PRESENT FUEL TO INDEPENDENTLY VERIFY THE WT WAS CORRECT; YES I SHOULD HAVE. WHY DID I NOT DO THIS? BECAUSE AT THAT TIME WE WERE ON THE ARR AND WE HAD AN ACFT WITHOUT A FUNCTIONING NAV SYS. WE WERE IN THE MIDDLE OF AN ARR PROC IN ZZZ1 AIRSPACE; WITH THE FO FLYING THE ACFT AND I WAS TRYING TO BACK UP THE PF. EVEN THOUGH THIS TYPE OF ERROR IS RARE IN OCCURRENCE; I BELIEVE THERE IS SOMETHING THAT CAN BE DONE TO PRECLUDE THIS TYPE OF MISTAKE FROM HAPPENING AGAIN. A CHANGE IN PROC THAT REQUIRES AN INDEPENDENT COMPUTATION OF THE LNDG WT WOULD PREVENT THIS MISCALCULATION. THIS WOULD BE USED IN CONJUNCTION WITH AN ADDED STEP IN THE APCH CHKLIST TO REFLECT THE SEPARATE VERIFICATION. HAD I LOOKED AT MY FMC; I WOULD HAVE KNOWN THE EXACT REASON FOR THE ALPHA DISPLAY. THIS IS A PERFECT EXAMPLE OF TRUSTING YOUR GUT FEELING AND PAYING ATTN TO WHAT THE ACFT IS TELLING YOU.