ORIGINAL: Rotaryphile
I used to build engine powered freeflight models that balanced on the trailing edge of the wing, but they had stabs with roughly 50% of the wing area. The important thing is to keep the CG slightly ahead of the center of pressure of the entire airplane, and those old freeflights had their center of pressure behind the wing trailing edge.
A hypothetical model with zero mass would probably be unstable, since the air influenced by the airplane has mass, and moves with the airplane. I have built models with wing loadings of well under one ounce per square foot, and their CG location is just as important as with far heavier wing loadings, and seems to like to be a little further forward than that of the heavier jobs. The mass of air influenced by a wing has a significant influence on flutter calculations. Flutter analysts frequently consider the mass of air influenced by a wing or stab to be roughly equal to that of a cylinder of air with radius equal to the wing chord.
Expanding on CG positions, the problem is that the center of pressure moves with airspeed (and angle of attack). If the CG is far back, I have found that as I dive (radio assist old timer contest free flight models to get back within time limits,) the CP (center of pressure) moves back, and it can get behind the CG. In a split second, the plane will tuck in and go inverted, often snapping the wing.
A heavy aircraft must fly at a greater angle of attack, and this moves the CP forward. This tends to pitch the nose up, and slow the plane down further, leading to a stall. With under cambered wings, a stall will be vicious, as the CP retreats rapidly from the forward position, aft. Even with a lifting tail-plane, one needs longitudinal dihedral to cope with shifting CP.