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.