AN EMB145 DEPARTED OVER WT FOR THE ACTIVE RWY AFTER THE FO CALCULATED ALLOWABLE WT FOR ANOTHER RWY.

Narrative

IT HAD BEEN A LONG DAY ALREADY WITH BAD WX FLYING IN AND OUT OF ZZZ1. AS WE LANDED IN ZZZ AND TAXIED IN AND PARKED; A TICKET AGENT BOARDED PRIOR TO DISEMBARKING THE PAX. HE ASKED US TO QUICKLY CALCULATE THE NUMBER OF PAX AND BAGS WE COULD TAKE ON THE OUTBOUND FLT TO ZZZ1 FROM ZZZ. THE FO'S DO THE WT AND BALANCE SO MY FO QUICKLY CHECKED THE WT RESTRICTION FOR TKOF BASED ON TEMP. HE THEN BACKED OUT THE NUMBERS USING THAT RESTRICTION. SHORTLY THEREAFTER; WE BOARDED AND SUBSEQUENTLY TOOK OFF FOR ZZZ1 USING RWY 29 (OTHER RWY WAS NOTAMED CLOSED). I NOTICED THAT WE USED MORE RWY THAN USUAL FOR OUR TKOF ROLL. I CHKED HIS NUMBERS AT CRUISE AFTER THINGS SETTLED DOWN AND FOUND THAT IN THE RUSH BACK AT THE GATE; HE ERRONEOUSLY HAD USED THE WT RESTRICTION FOR RWY 02. THE FLT WENT SMOOTH AND WITHOUT INCIDENT; FORTUNATELY. THIS WAS A GRIEVOUS ERROR ON MY PART BECAUSE AS THE PIC; I SHOULD HAVE SLOWED THE PACE OF THINGS FOR SAFETY AND CHKED HIS WORK AS WELL. (RWY 29 IS 6525 FT LONG; THE OTHER RWY IS 8000 FT LONG.)'