  We combine histogram reweighting techniques with the two-lattice matching
Monte Carlo renormalization group method to conduct computationally efficient
calculations of critical exponents on systems with moderately small lattice
sizes. The approach, which relies on the construction of renormalization group
mappings between two systems of identical lattice size to partially eliminate
finite-size effects, and the use of histogram reweighting to obtain
computationally efficient results in extended regions of parameter space, is
utilized to explicitly determine the renormalized coupling parameters of the
two-dimensional $\phi^{4}$ scalar field theory and to extract multiple critical
exponents. We conclude by quantifying the computational benefits of the
approach and discuss how reweighting opens up the opportunity to extend Monte
Carlo renormalization group methods to systems with complex-valued actions.
