In 1965 Borwein presented the concept of strongly summable single valued functions. Using Borwein's results, in 2019 Patterson et all. introduced the notion of multidimensional linear functions connected with double strongly Cesaro summability theory. The aim of this study is to extend Patterson et all's results to strongly summable bivariate functions with respect to weight of g. To achieve this by considering a real valued non-negative bivariate measurable function defined on the interval (1,∞)×(1,∞) the concepts of double [W_(λ,μ)^g ]_f -strongly summable and [S_(λ,μ)^g ]_f-double statistical convergence of weight g will be introduced, where g:[0,∞)×[0,∞)→[0,∞) such that g(x_m,x_n )→∞ as x_m→∞ and x_n→∞. Also g is factorable. In addition, the relationship between these two concepts will be examined and some algebraic characterization of real valued lebesgue measurable bivariate functions will be also presented.