In statistical mechanics, the statistical weight is the relative probability (possibly unnormalized) of a particular feature of a state. If the energy associated with the feature is ΔE, the statistical weight is given by the Boltzmann factor e−ΔE/kT, where k is the Boltzmann constant and T is the temperature in kelvins.
The statistical weight is a convenient shorthand that is often used in transfer matrix solutions of problems in statistical mechanics.
References
Statistical weight Wikipedia(Text) CC BY-SA