This paper presents a Weyl-invariant Einstein-Cartan gravity theory that unifies the strong CP problem and the hierarchy puzzle. The minimal Weyl-invariant Einstein-Cartan gravity combined with the Standard Model contains one extra scalar degree of freedom, an axion-like particle (ALP), which can solve the strong CP problem. The smallness of the ALP mass and the cosmological constant is ensured by the tiny values of the gauge coupling constants of the local Lorentz group. The tree-level Higgs mass and Majorana lepton masses are very small or vanishing, allowing for their computability via nonperturbative effects. The theory automatically accommodates a coupling of the ALP to the topological charge density of QCD, enabling a purely gravitational solution to the strong CP problem. The ALP's mass is gravitationally induced, and its coupling to the QCD anomaly allows for a solution to the strong CP problem. The theory also provides a mechanism for generating heavy neutral leptons in the early universe, which could account for dark matter. The theory is fully compatible with the neutrino Minimal Standard Model and provides a gravitational origin for the ALP. The paper also discusses the implications of the theory for cosmology, including the possibility of inflation and dark matter. The theory is shown to have a positive-definite Euclidean action, allowing for a consistent path-integral formulation. The paper concludes that the theory provides a remarkably economical description of all known interactions and offers a self-consistent and purely gravitational origin for the ALP.This paper presents a Weyl-invariant Einstein-Cartan gravity theory that unifies the strong CP problem and the hierarchy puzzle. The minimal Weyl-invariant Einstein-Cartan gravity combined with the Standard Model contains one extra scalar degree of freedom, an axion-like particle (ALP), which can solve the strong CP problem. The smallness of the ALP mass and the cosmological constant is ensured by the tiny values of the gauge coupling constants of the local Lorentz group. The tree-level Higgs mass and Majorana lepton masses are very small or vanishing, allowing for their computability via nonperturbative effects. The theory automatically accommodates a coupling of the ALP to the topological charge density of QCD, enabling a purely gravitational solution to the strong CP problem. The ALP's mass is gravitationally induced, and its coupling to the QCD anomaly allows for a solution to the strong CP problem. The theory also provides a mechanism for generating heavy neutral leptons in the early universe, which could account for dark matter. The theory is fully compatible with the neutrino Minimal Standard Model and provides a gravitational origin for the ALP. The paper also discusses the implications of the theory for cosmology, including the possibility of inflation and dark matter. The theory is shown to have a positive-definite Euclidean action, allowing for a consistent path-integral formulation. The paper concludes that the theory provides a remarkably economical description of all known interactions and offers a self-consistent and purely gravitational origin for the ALP.