CRJ700 Captain discovers CG to be out of limits during manual weight and balance calculation. Problem is traced to incorrect balance arm calculated after most recent aircraft reweigh. Maintenance and dispatch are unaware of the new number.

Narrative

We were preparing the weight and balance information when we noticed a discrepancy. The ACARS on the plane was written up as inoperative; but reported as working by the previous crew; however; apparently the trim setting was contradicting the paper weight and balance. Since it was inoperative; I had the First Officer fill out a paper weight and balance form; but still decided to fill out the ACARS to see what sort of number came up. The flight was full with standard number of bags; but after the First Officer did the paperwork; it was showing that the plane was out of center of gravity; too far forward. This was very curious and should not have been the case with our load. We both reworked the numbers several times and repeatedly came up with the same answer. The numbers from the ACARS were showing normal; however. While inspecting the weight and balance information; I noticed that the plane had apparently been reweighed and given a new BOW and BOW AMU just 7 days prior. I called maintenance to see what number they had since I was certain it had to be a typo. They said their computer showed no record of a reweigh and had numbers from 2007. Using the previous BOW AMU; we re-ran the numbers and the center of gravity and trim settings came back normal and matching with the ACARS. We told maintenance to look into and just used those old numbers and departed. Upon arriving; I called maintenance again to see what they found and they had no new information and asked me to fax the page from the trip to them; so they could investigate with quality control. I informed the new crew picking up the plane of the situation and left for the hotel. The following day; I ran into the First Officer that had taken the plane from me and said that they had sat for over 1 hour trying to figure it out. Apparently; when they reweighed it; they had the BOW and moment; but did incorrect math in acquiring the AWU. With the correct math; the crew was given the new correct AWU that was slightly different from the old; much different from the 'new' and worked out perfectly; including matching the ACARS. I'm still not sure why maintenance had no record of the reweigh and find it somewhat disturbing that this plane had been signed off for service with such faulty weight and balance information. If someone had flown the trim settings using that new number it would have been grossly out of place. I also realize I should have investigated further before leaving; but did not realize at the time the magnitude of the situation.