JohnBuckner is correct. If a plane is nose-heavy it is more stable in flight. If it is tail-heavy, then it could be uncontrollable. However, if it is too nose-heavy then you will run out of elevator control on landing an it will dive in at the last second.

That's not a big deal, just ugly. If that happens, then you should move your CG back about 1/4" at a time until it stops happening. If the plane starts getting too twitchy on the elevator, then you may need to reduce the elevator throw a little or move the CG back to where it was previously. Your instructor should be able to let you know what you need to do to improve the flight qualities of your trainer.