By generically constraining the boundary term of the action of gravity, the formal structure of the observed types of matter fields (scalar, fermion/Dirac and spin 1) is obtained in the weak gravity limit, including their gauge behaviour, covering the standard model. By gravity, we mean any theory having the Gibbons-Hawking-York boundary term as its torsion-free weak gravity limit. The constraining term is assumed to be local, not explicitly coordinate-dependent and to be the boundary term of a bulk function (Lagrangian). In this way, the latter is fixed to a large extent, admitting couplings and mass terms. The formal matching with observed fields suggests that matter should be the consequence of gravity constraining, and quantum matter would result from constrained quantum gravity. This implies that it is possible to compute the value of 6.564.10^{-69} m^2 for the fundamental quantum constant of gravity - the smallest possible change of the boundary term. Also, the freedom to construct a fundamental quantum concept of gravity is strongly reduced, and the weak gravity limit is completely determined. For strong gravity, the boundary term - rather than the Hamiltonian - yields a key quantum counting operator.