This paper presents new spectral generalizations of the classical Bishop–Gromov volume comparison theorem and Bonnet–Myers theorem, along with applications to isoperimetry. The authors show that if a closed Riemannian manifold $ (M, g) $ of dimension $ n \geq 3 $ satisfies the spectral condition $ \lambda_1(-\frac{n-1}{n-2}\Delta + \mathrm{Ric}) \geq n-1 $, then the volume of $ M $ is bounded above by the volume of the $ n $-dimensional sphere $ \mathbb{S}^n $, and the fundamental group $ \pi_1(M) $ is finite. The constant $ \frac{n-1}{n-2} $ is optimal, and if the volume of $ M $ equals that of $ \mathbb{S}^n $, then $ M $ is isometric to $ \mathbb{S}^n $. A sharp generalization of the Bonnet–Myers theorem is also established 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 infers sharp results on the isoperimetric structure at infinity of complete manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature. The paper also discusses the implications of the spectral condition on the isoperimetric profile and volume bounds of manifolds. It shows that under the given spectral condition, the isoperimetric profile satisfies a sharp inequality, leading to a sharp volume bound. The diameter bound is obtained using a $ \mu $-bubble approach, which is a generalization of the Gromov's $ \mu $-bubble method. The paper concludes with a discussion of the implications of the results for the isoperimetric structure of manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature, and it raises an open question about the existence of such manifolds in higher dimensions. The results have applications to geometric problems, including the stable Bernstein problem and the study of manifolds with uniform Kato bounds on the Ricci curvature.This paper presents new spectral generalizations of the classical Bishop–Gromov volume comparison theorem and Bonnet–Myers theorem, along with applications to isoperimetry. The authors show that if a closed Riemannian manifold $ (M, g) $ of dimension $ n \geq 3 $ satisfies the spectral condition $ \lambda_1(-\frac{n-1}{n-2}\Delta + \mathrm{Ric}) \geq n-1 $, then the volume of $ M $ is bounded above by the volume of the $ n $-dimensional sphere $ \mathbb{S}^n $, and the fundamental group $ \pi_1(M) $ is finite. The constant $ \frac{n-1}{n-2} $ is optimal, and if the volume of $ M $ equals that of $ \mathbb{S}^n $, then $ M $ is isometric to $ \mathbb{S}^n $. A sharp generalization of the Bonnet–Myers theorem is also established 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 infers sharp results on the isoperimetric structure at infinity of complete manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature. The paper also discusses the implications of the spectral condition on the isoperimetric profile and volume bounds of manifolds. It shows that under the given spectral condition, the isoperimetric profile satisfies a sharp inequality, leading to a sharp volume bound. The diameter bound is obtained using a $ \mu $-bubble approach, which is a generalization of the Gromov's $ \mu $-bubble method. The paper concludes with a discussion of the implications of the results for the isoperimetric structure of manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature, and it raises an open question about the existence of such manifolds in higher dimensions. The results have applications to geometric problems, including the stable Bernstein problem and the study of manifolds with uniform Kato bounds on the Ricci curvature.