Rotational Energy Levels
First, take a look at classical physics. The angular momentum of a particle rotating in a plane is defined as
$$L = I \omega$$
and its kinetic energy is
$$E = \frac{1}{2} I \omega^2 = \frac{L^2}{2I}.$$

So if you formulate your energy in terms of the angular momentum of your rotating particle, you arrive at the inverse relation. 

In analogy to the classical picture, the eigenvalues of the rotational Schrödinger equation,
$$ E = hcBJ(J+1),$$
likewise depend quadratically on the angular momentum quantum number, and thus have a similar inverse dependence on the moment of inertia through $B$.