For a finite abelian group G with exp(G) = n, the arithmetical invariant sA(G) is defined to be the least integer k such that any sequence S with length k of elements in G has a A weighted zero-sum subsequence of length n. When A = {1}, it is the Erdős-Ginzburg-Ziv constant and is denoted by s(G). For certain class of sets A, we already have some general bounds for these weighted constants corr...