The paper presents a spectral generalization of the classical Bishop–Gromov volume comparison theorem and the Bonnet–Myers theorem for closed Riemannian manifolds. Specifically, it shows that if a closed Riemannian manifold $(M, g)$ of dimension $n \geq 3$ satisfies the spectral condition \[ \lambda_1 \left( -\frac{n-1}{n-2} \Delta + \text{Ric} \right) \geq n-1, \] then the volume of $M$ is bounded above by the volume of the unit sphere $\mathbb{S}^n$, and the fundamental group $\pi_1(M)$ is finite. The constant $\frac{n-1}{n-2}$ is sharp, and if the equality holds, $M$ is isometric to $\mathbb{S}^n$. Additionally, the paper provides a sharp generalization of the Bonnet–Myers theorem under the same spectral condition. The proofs involve the use of a new unequally weighted isoperimetric problem and unequally warped $\mu$-bubbles. As an application, in dimensions $3 \leq n \leq 5$, the paper derives sharp results on the isoperimetric structure at infinity for complete manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature. These results include a sharp upper bound on the isoperimetric profile and a conclusion about the linear volume growth of the manifold at infinity. The paper also discusses the implications of these results for the stable Bernstein problem and the study of manifolds with uniform Kato bounds on the Ricci curvature. The proofs are detailed and include Lemmas and Corollaries that support the main theorems.The paper presents a spectral generalization of the classical Bishop–Gromov volume comparison theorem and the Bonnet–Myers theorem for closed Riemannian manifolds. Specifically, it shows that if a closed Riemannian manifold $(M, g)$ of dimension $n \geq 3$ satisfies the spectral condition \[ \lambda_1 \left( -\frac{n-1}{n-2} \Delta + \text{Ric} \right) \geq n-1, \] then the volume of $M$ is bounded above by the volume of the unit sphere $\mathbb{S}^n$, and the fundamental group $\pi_1(M)$ is finite. The constant $\frac{n-1}{n-2}$ is sharp, and if the equality holds, $M$ is isometric to $\mathbb{S}^n$. Additionally, the paper provides a sharp generalization of the Bonnet–Myers theorem under the same spectral condition. The proofs involve the use of a new unequally weighted isoperimetric problem and unequally warped $\mu$-bubbles. As an application, in dimensions $3 \leq n \leq 5$, the paper derives sharp results on the isoperimetric structure at infinity for complete manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature. These results include a sharp upper bound on the isoperimetric profile and a conclusion about the linear volume growth of the manifold at infinity. The paper also discusses the implications of these results for the stable Bernstein problem and the study of manifolds with uniform Kato bounds on the Ricci curvature. The proofs are detailed and include Lemmas and Corollaries that support the main theorems.