The physical content of the three more natural models ofGL(4) gravity is analyzed, for the case of weak fields. The first model we deal with is the linearized version of Yang's onetensor-field gravity. It is shown that this is a scalar-tensor theory, with its scalar part contained in the symmetric tensorhαν, instead of appearing explicitly, externally to the symmetric tensorhαν, as happens in Brans-Dicke type of scalar-tensor theories. The second and the third linearized models, which can both be derived from the fourth-order action postulated by Yang, turn out to be two-tensor decoupled systems. In both cases one of the tensors is the symmetric weak metric gravity tensor field. The second tensor appearing in these two models, representing theGL(4)-gauge field, is either a linearized symmetric affinity (in the second model) or a linearized but nonsymmetric affinity (for the third model). It is shown that in these last two cases the affinity contains a helicity-3 propagating field. The connection is also given between the fourth-order system which determines the dynamical structure (for the last two models) of the metric tensor and the third-order Yang model of gravity. Owing to the presence of helicity-3 fields we show that it is better to regard Yang's action as an action for a two-tensor system instead of trying to recover from it a pure gravity (one-tensor-field) action. Finally, it is shown what is the dynamical structure of the second and third linearized two-tensor models which can be derived from Yang's action.