  We study universal features of the density of one-particle states $\rho(E)$
in weakly coupled theories of gravity at energies above the quantum gravity
cutoff $\Lambda$, defined as the scale suppressing higher-derivative
corrections to the Einstein--Hilbert action. Using thermodynamic properties of
black holes, we show that in asymptotically flat spacetimes, certain features
of $\rho(E)$ above the black hole threshold $M_{\rm min}$ are an indicator for
the existence of large extra dimensions, and cannot be reproduced by any
lower-dimensional field theory with finitely many fields satisfying the weak
energy condition. Based on the properties of gravitational scattering
amplitudes, we argue that there needs to exist a (possibly higher-dimensional)
effective description of gravity valid up to the cutoff $\Lambda$. Combining
this with thermodynamic arguments we demonstrate that $\rho(E)$ has to grow
exponentially for energies $\Lambda \ll E \ll M_{\rm min}$. Furthermore we show
that the tension of any weakly coupled $p$-brane with $p\geq 1$ is bounded from
below by $\Lambda^{p-1}$. We use this to argue that any tower of weakly coupled
states with mass below $\Lambda$ has to be a Kaluza--Klein (KK) tower.
Altogether these results indicate that in gravitational weak-coupling limits
the lightest tower of states is either a KK tower, or has an exponentially
growing degeneracy thereby resembling a string tower. This provides evidence
for the Emergent String Conjecture without explicitly relying on string theory
or supersymmetry.
