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We find the Hamiltonian expression in the York basis of canonical ADM tetradgravity of the 4-Weyl tensor of the asymptotically Minkowskian space-time. Likefor the 4-Riemann tensor we find a radar tensor (whose components are 4-scalarsdue to the use of radar 4-coordinates), which coincides with the 4-Weyl tensoron-shell on the solutions of Einstein's equations. Then, by using theHamiltonian null tetrads, we find the Hamiltonian expression of the Weylscalars of the Newman-Perose approach and of the four eigenvalues of the 4-Weyltensor.  After having introduced the Dirac observables of canonical gravity, whosedetermination requires the solution of the super-Hamiltonian and super-momentumconstraints, we discuss the connection of the Dirac observables with the notionof 4-scalar Bergmann observables. Due to the use of radar 4-coordinates thesetwo types of observables coincide in our formulation of canonical ADM tetradgravity. However, contrary to Bergmann proposal, the Weyl eigenvalues are shownnot to be Bergmann observables, so that their relevance is only in their use(first suggested by Bergmann and Komar) for giving a physical identification aspoint-events of the mathematical points of the space-time 4-manifold.  Finally we give the expression of the Weyl scalars in the HamiltonianPost-Minkowskian linearization of canonical ADM tetrad gravity in the family of(non-harmonic) 3-orthogonal Schwinger time gauges.

Hamiltonian Expression of Curvature Tensors in the York Canonical Basis:  II) The Weyl Tensor, Weyl Scalars, the Weyl Eigenvalues and the Problem of  the Observables of the Gravitational Field