MO Diagram "greatest stabilisation when orbitals are close in energy"
Fundamentally it's mathematics. The energies of the MOs are the eigenvalues of the matrix $$\begin{pmatrix}\alpha_1 &amp; \beta \\ \beta &amp; \alpha_2 \end{pmatrix},$$ where $(\alpha_1,\alpha_2)$ are the energies of the two constituent orbitals and $\beta$ is (loosely speaking) the overlap between them.

For the same size of $\beta$, if $\alpha_1 \approx \alpha_2$, then the eigenvalues can differ quite a lot from $(\alpha_1,\alpha_2)$. On the other hand, if $\alpha_1$ is very different from $\alpha_2$, then the eigenvalues will be closer to $(\alpha_1,\alpha_2)$.

As an illustration consider the matrix

$$\begin{pmatrix}1.1 &amp; 0.5 \\ 0.5 &amp; 1 \end{pmatrix}$$

This has eigenvalues of $1.55$ and $0.55$, which are relatively distant from the "original energies" of $1.1$ and $1$. On the other hand, the matrix

$$\begin{pmatrix}3 &amp; 0.5 \\ 0.5 &amp; 1 \end{pmatrix}$$

has eigenvalues $3.12$ and $0.88$, which are closer to $3$ and $1$.

Taking a more abstract perspective, the eigenvalues of $$\begin{pmatrix}\alpha_1 &amp; \beta \\ \beta &amp; \alpha_2 \end{pmatrix}$$ are

$$\lambda_\pm = \frac{\alpha_1 + \alpha_2}{2} \pm \frac{\sqrt{(\alpha_1 - \alpha_2)^2 + 4\beta^2}}{2}$$

and you can play around with this expression to gain some insight. For example, in the limit where  $(\alpha_1 - \alpha_2)^2 \gg 4\beta^2$ (corresponding to a large energy difference between the original interacting orbitals), the eigenvalues reduce to

$$\lambda_\pm \to \frac{\alpha_1 + \alpha_2}{2} \pm \frac{\alpha_1 - \alpha_2}{2}$$

which are simply $\alpha_1$ and $\alpha_2$.