  The linear approximation of scalar-tensor theories of gravity is obtained in
the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then
the weak-field limit is analyzed and the conditions leading to significant
deviations of the $1/r^{2}$ Newton's law of gravitation are discussed. Finally,
the scalarization effects induced by these theories in extended objects are
confronted within the weak-field limit.
