Among other parameters ( runway length, airpressure, air temperature, runway condition, wind speeds and wind direction, etc. ) the C.G. ( Center of Gravity ) is crucial for computing the stabilizer setting (if you look closely, you'll see that the horizontal stabilizers at the aircraft tail aren't fixed - the can be 'swiveled' within a certain range) , the speed at which the crew can abort the take-off run with enough runway left to bring the plane to a stop, the speed at which they can rotate ( get airborne ) safely, and the speed at which they have to rotate to avoid making a hole in the ground.
Moving about during the take-off run would muck up these careful computations , in the worst case to a point where safety would be adversely effected. Take-off speed is comparatively slow compared to cruising speed, so once the plane has reached a certain altitude and speed, the C.G. isn' t that crucial anymore - in fact it's shifting continously while in flight as fuel is burned off; the stabilizers will offset that shift by repositioning themselves.
There have been incidents with cargo planes, where cargo had torn loose during take-off, the sudden shift in C.G. causing tail strikes.