The amount of Cm indicates how large a tail volume you need. That's not how fat the rear of the fuselage is but rather how long the tail is compared to how large the stab is.

For example a flying wing airfoil like the MH110 will show a positive curve indicating that it's stable without any other tail. Low pitching moment values will tell you that you can get away with less than normal. Symetrical wings for example hardly need any tail. Especially if the balance is anywhere near the 25% chord point. Of course the amount of tail will also determine the response to control inputs so that's why you see lots of models with very large stabs and elevators even with a symetrical airfoil.

BTW. If you play with a little test wing all by itself you'll see the outcome of the negative moments. Build a couple of 3 x 12 x 1/16 sheet balsa wings. One curved with ribs to a conventional airfoil arc of about 1/8 inch and the other with a forward high point of the same 1/8 inch but at the 15% mark and with a 1/16 reflex curve at the rear 1 inch mark. Try gliding them and they will both flip up (usually) or down (sedom but it depends on how you launch them) and watch them flip like a dervish. Now start adding nose weight to get the balance to near the 25% mark. At some point the arced wing will tuck violently and nothing you do will make it fly stably. Removing some weight helps but it goes from less violent tuck under to the upwards back flipping in the blink of an eye.

The reflexed wing will respond to nose weight by starting to act almost normal with a stalling flight transitioning to a normal flight as you move the balance forwars and finally to a controlled dive.

All because the reflex makes the section have a positive Cm rather than a negative one.