In this study, we define new paranormed sequence spaces by combining a generalized weighted mean and a difference operator. Furthermore, we compute the alpha-,beta- and gamma- duals and obtain bases for these sequence spaces. Besides this, we characterize the matrix transformations from the new paranormed sequence spaces to the spaces c(0)(q), c(q), l(q) and l(infinity)(q). Finally, weighted core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core. (c) 2012 Elsevier Ltd. All rights reserved.