This work introduces the novel flat-histogram Monte Carlo (MC) method stochastic approximation with a dynamic update factor (SAD) and explores the convergence properties of a variety of related weight-based MC methods. The new method is applied to a number of physical `test’ systems including the 2D Ising model, a square-well fluid, and a Lennard-Jones cluster. A driving motivation for developing novel Monte Carlo methods that have physically based tunable parameters is to provide simulation methods for exploring metal-organic frameworks (MOFs). A theoretical framework for gas adsorption and delivery in metal-organic frameworks is developed and compared with experimental data. SAD is introduced as a powerful method for examining thermodynamic properties for MOFs. A preliminary groundwork is laid for the future development of a multi-dimensional SAD which would be able to compute all properties of interest for any given MOF thereby providing a powerful way for researchers to determine any porous media's suitability for gas storage applications.