  We develop a general approach to calculating "nonuniversal" prefactors in
static and dynamic correlation functions of 1D quantum liquids at zero
temperature, by relating them to the finite size scaling of certain matrix
elements (form factors). This represents a new, powerful tool for extracting
data valid in the thermodynamic limit from finite-size effects. As the main
application, we consider weakly interacting spinless fermions with an arbitrary
pair interaction potential, for which we perturbatively calculate certain
prefactors in static and dynamic correlation functions. We also
non-perturbatively evaluate prefactors of the long-distance behavior of
correlation functions for the exactly solvable Lieb-Liniger model of 1D bosons.
