Consider a finite abelian group G (written additively). A sequence \(S=(g_1, \ldots ,g_l)\) over G is called a zero-sum sequence if \(g_1+\cdots +g_l =0,\) where 0 is the identity element of the group. Inspired by a well known result of Erdős, Ginzburg and Ziv, and some questions of K. Rogers and Davenport related to factorization in number fields, the area of zero-sum theorems in combinatorial number theory has seen a rapid growth in recent years. The area of zero-sum theorems has many interesting results and several unanswered questions. Several authors have introduced interesting elementary algebraic techniques to deal with these problems. We describe some experiments with these elementary algebraic methods and some combinatorial ones, in a weighted generalization of some extremal problems in the area of Zero-sum Combinatorics.