  The reweighting method is widely used in numerical studies of QCD, in
particular, for the cases in which the conventional Monte-Carlo method cannot
be applied directly, e.g., finite density QCD. However, the application range
of the reweighing method is restricted due to several problems. One of the most
severe problems here is the overlap problem. To solve it, we examine a
multipoint reweighting method in which simulations at several simulation points
are combined in the data analyses. We systematically study the applicability
and limitation of the multipoint reweighting method in two-flavor QCD at zero
density. Measuring histograms of physical quantities at a series of simulation
points, we apply the multipoint reweighting method to calculate the meson
masses as continuous functions of the gauge coupling $\beta$ and the hopping
parameters $\kappa$. We then determine lines of constant physics and beta
functions, which are needed in a calculation of the equation of state at finite
temperature.
