A321 pilot reported fuel transfer pumps were malfunctioning and fuel was venting from left wing resulting in a fuel imbalance and overweight landing

Narrative

Departed ZZZ at XA09 with MEL 28-XX-XX (L Center Tank transfer valve inop). The L Center Tank pump was confirmed in the closed position per MEL compliance during preflight. Fuel at takeoff was 44.0 lbs. 27 minutes after takeoff we received an ECAM Fuel CTR L XFR FAULT". Both ECAM AND QRH were completed. CTR L XFR pb turned OFF. 37 minutes after takeoff; we received an ECAM "Fuel L WING TK OVERFLOW". ECAM and QRH were completed. Left wing tank pumps were turned off. L CTR XFR pb from previous ECAM remained in OFF position. However; left wing tank quantity continued to rise. Manual calculations were made comparing [FOB + Fuel used] to [Fuel at takeoff]. Calculations showed a continuous fuel deficit occurring. Upon landing; a deficit of 1;340 lbs was noted. Attempt to balance the fuel per QRH to assist in troubleshooting was also attempted with no success. Dispatch and Maintenance Control were contacted via SATCOM. Troubleshooting was unsuccessful and a divert to ZZZ1 was agreed upon. ATC [provided priority handling] for us to provide expedited handling. Divert and overweight checklists were completed and briefed. Inflight was briefed. Passengers were briefed. Approach and landing to runway XXC was uneventful. Aircraft landed 200 pounds overweight with a touchdown VSI of 100fpm or less. Logbook entries were made for associated ECAMs and overweight landing. Contract Mx (Maintenance) in ZZZ1 confirmed the left wing overflow disc was missing from the left wing confirmed fuel had likely been venting overboard."