An A320 pilot received final weights from ground personnel shortly after takeoff.

Narrative

We received final weights just as we began our taxi to Runway 34R at DEN. Other than a slight ZFW weight increase that prompted me to call up new runway data in ACARS; there was nothing unusual or unexpected in the final weight printout. The taxi out and takeoff were uneventful. During the climb out; I noticed a flashing ACARS MSG and eventually pulled up the message from Load Planning: 'Your Weights are Invalid. New final weights are required before takeoff.' This message was time-stamped two and a half minutes after our takeoff. We exchanged messages with Load Planning; and received the new final weight printout. While the passenger count and ZFW had not changed; we noticed that the MAC had moved forward; from 33.4% to 31.5%. We entered the new data into the FMGC; and proceeded uneventfully to our destination. Our ACARS exchange with Load Planning indicated that they had received a last-minute change from the ramp. While this was a minor change with little impact on our flight; the possible safety ramifications of an aircraft taking off with inaccurate final weights/trim are obvious.