Why is managing CG (centre of gravity) important?
To balance the aircraft, the sum of the lift from all lifting surfaces has to be at the same position as the weight. If the c.g. is ahead of the center of lift, the aircraft will pitch down. The pilot can counteract this by pulling on the elevator, which in effect reduces lift at the tail and thus shifts the center of lift forward. As you can imagine, there is only so much lengthwise change which can be effected with the elevator. So the first limit for the c.g. position is given by controllability.
Another important consideration is stability. You want the airplane to return to the original flight attitude if it has been disturbed, say by jolt on the stick or yoke. This can be done by creating proportionally more lift with the forward surfaces (= the wing in a conventional configuration) than with the tail surfaces. Say the jolt pitches the aircraft up. Now the aerodynamic forces should change in a way which increases lift proportionally more on the tail surfaces, so the aircraft pitches down and returns to it's original attitude. By distributing lift the way I mentioned above, the same change in angle of attack on both wing and tail will create a proportionally higher lift increase on the tail, making the aircraft (statically) stable. Thus, the second important limit for c.g. location is stability.
As for tipping over …