A B737-300 CREW TOOK OFF OVERWT AT BOS BECAUSE OF TIME PRESSURES AND CONFUSING COMPANY PROC.

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PREDEP REVIEW OF TKOF PERFORMANCE SYS (TPS) DEP PLAN INDICATED WE WERE LEGAL TO DEPART ON RWY 27 WITH ENG BLEEDS OFF; 124 PAX AND FUEL OF 21600 LBS. DURING SINGLE ENG TAXI OUT; FINAL WT AND BAL MESSAGE DID NOT ARRIVE. AFTER START OF SECOND ENG; WT AND BAL MESSAGE FINALLY CAME WITH ONLY RWY 33L INDICATED AND ONLY 2 ACFT IN USE FOR DEPS. WE HAD NOW ADVANCED TO NEXT FOR TKOF; SO WE AGAIN CHKED THE TPS TO RECONFIRM RWY 27 LEGALITY. THE FUEL LOAD HADN'T CHANGED AND PAX COUNT HAD INCREASED BY 1 PAX. INEXPLICABLY; THE GROSS TKOF WT HAD INCREASED BY ABOUT 5500 LBS WHICH WENT UNNOTICED EVEN THOUGH WE RESET THE TKOF SPDS TO REFLECT THE HIGHER WT. WE THEN PERFORMED THE BLEEDS OFF TKOF ON RWY 27 WHEN CLRED BY BOS TWR. ACFT WE PICKED UP ARRIVED APPROX 90 MINS LATE; CAUSING COMPRESSED TIME TO COMPLETE ALL REQUIRED PREFLT CHKS. SUBSEQUENT DEP WAS 1 HR 35 MINS LATE. AUTOMATIC PDC ISSUED AN RNAV DEP WHICH FO HAD TO VERBALLY DECLINE WHICH RESULTED IN A NEW CLRNC ISSUED REQUIRING READBACK. DURING SINGLE ENG TAXI OUT; GND CTL INSTRUCTED US TO AGAIN CALL CLRNC DELIVERY. WE THEN RECEIVED A COMPLETELY NEW WX RELATED RERTE NECESSITATING ANOTHER FULL RTE READBACK; ENTERED NEW RTE IN FMS COMPUTER; AND VERIFIED WITH COMPANY DISPATCHER THAT NEW RTE WAS ACCEPTABLE. THEREFORE; FO'S 'HEADS DOWN' TIME WAS GREATLY INCREASED WHILE CAPT HANDLED THE COMS WITH GND AND TWR WHILE TAXIING ON THE PRESCRIBED RTE WHICH INCLUDED THE XING OF RWYS 22L; 22R; AND 33L WHICH WAS BEING USED FOR LNDGS. ADDITIONAL FACTORS WERE THE AFOREMENTIONED START OF THE SECOND ENG AND ASSOCIATED CHKLISTS COUPLED WITH THE LATE ARR OF THE FINAL WT AND BAL MESSAGE. MORE THOROUGH REVIEW OF THE TKOF PERFORMANCE SYS DEP PLAN AND FINAL WT AND BAL MESSAGE DURING THE CLBOUT ABOVE 10000 FT MSL WHEN FLT DECK WORKLOAD WAS GREATLY REDUCED. CESSATION OF USING THE TPS TO VERIFY TKOF LEGALITY WHEN A DIFFERENT RWY IS XMITTED ON THE FINAL WT AND BAL MESSAGE AFTER TAXIING HAS BEGUN. IF 2 HIGHLY EXPERIENCED AND DILIGENT PLTS CAN MAKE THIS ERROR OF OMISSION; I BELIEVE THIS COMPANY ENCOURAGED TRAINING PRACTICE AND CONFUSING PROC TO BE SERIOUSLY FLAWED.