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If you would show us a screenshot of the problem you are having, we can help.
If you're talking about static balance, then this is entirely consistent with expected behaviour. Small variations (and we're talking about a matter of INCHES in the real-world situation) in displacement of CoL relative to CoM, as well as CoL vector incidence to CoL-CoM arm & relative airflow etc, manifest in relatively large variations of the aircraft's in-flight static condition.
It is not infeasable that an aircraft be rendered unflyable by an out-of-balance condition of only 6 inches of CoM displacement, depending on the type design.
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If you're talking about the fuselage's angle of incidence to the relative airflow, then you'll need to take into account not only the CoL vector of the main wing but that of any horizontal stabs as well. Horizontal stabs have long moment arms so small vector variations produce proportionally larger effects. Main wings have large vector magnitudes so small changes also produce proportionally larger effects.
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It certainly has it's deficiencies & errors etc, however the game appears at least approximately correct, in the *general case*, with CoM & CoL relationship. If I make a change in-hangar, the result I see in-simulation appears pretty much as I might expect... at least up to a point.
Whether or not a plane 'should fly' can't be determined purely from the location of the markers.
There are any number of possible reasons why your plane won't take off, including but in no way limited to: Low Lift/Mass index (ie too heavy or not enough wing area), Low Lift/Drag index (too much drag for the lift it produces), Low Thrust/Drag index, Main gear located too far from CoM, Wing incidences poorly configured, Incorrectly placed/configured/missing control surfaces... just off the top of my head.
For example: http://tinypic.com/m/jjl0dz/2
My center of lift in that picture is located slightly behind and roughly level with the center of mass. This gives the plane a desire to nose down slightly in front. Placing the center of lift behind the center of mass is generally considered the optimal placement for most people. The closer the center of lift is to the center of mass, the more maneuverable but less stable the plane will be. Planes with the center of lift ahead of the center of mass tend to be harder to fly, and can be prone to going nose up very steeply on takeoff and back flipping into the ground.
Also note that my rear landing gear is just behind the center of mass. Not clear in the picture, but the landing gear is also slightly shorter in the rear than the front (because it's mounted higher). This makes takeoff as easy as possible for a design like this one that uses a tail for pitch control.
If you need to have the rear landing gear right at the back, use canards instead of a tail fin. With enough lift and speed, canards can lift the nose off the ground. You should avoid making a plane that sits nose down on the runway. You'll need to rotate the wings to generate positive lift in this configuration if you decide to go that route.
http://puu.sh/qCr4H/5c1349707f.jpg
http://puu.sh/qCrj8/c446e0ec43.jpg
Could it be too heavy? I does weight 15 ton.
Try moving your landing gear closer to your center of mass. If they're too far back, the aircraft won't be able to pivot on them.