Consider if we have a simple two-level toy model, where the ground state has energy $E_0 = 0$ and the excited state has energy $E_1 = \epsilon$ and degeneracy $g$. The partition function for this system is $$Z = 1 + g e^{-\beta \epsilon}$$ where $\beta = 1/k_BT$. The probability of a particle being in any of the excited states at a temperature $T$ is given by $$P(\epsilon) = \frac{ge^{-\beta \epsilon}}{1 + ge^{-\beta \epsilon}}$$ which for various $g$ looks like
My question is, why does having a higher degeneracy of the excited state mean it is more likely to be populated at a given temperature? What physical principle tells us this should be so?