An MD80 Captain reported that he took off with incorrect weight and balance figures because of a 1300 pound error. Company did not notify him until arrival at the next airport.

Narrative

We were handed the bag sheet at the gate prior to push back; which indicated 43 bags in the aft bin and 22 bags plus 200lbs in the middle bin. As we got the final numbers for the PAX count; the First Officer called for an automated weight & balance where we had questioned the Zero Fuel Weight. We both had determined that the reason for the lower Zero Fuel Weight was due to the low bag count. I taxied to the runway where we lined up for departure and transferred the controls to the First Officer for takeoff. On the takeoff roll; the gate agent called the tail number of the airplane. After takeoff we called back with the departure numbers and were never told that there was a bag discrepancy in the mid bin. Upon landing and parking at the gate; I had a voice message to call the gate agent in [departure station]. At that point she had informed me that there was fourty more bags in the middle bin that were not noted on the bag sheet and she had notified the station manager and Ops. My First Officer and I had determined that we were 1300lbs heavier than we thought and our takeoff stab trim was 3.11 units off. I believe that somebody at some point during the flight should have notified us that there was a bag discrepancy so we could have made the proper landing adjustments and determined if we were still within C.G. [limits].