In this paper we continue our investigation of the recent summability notion introduced in [Math. Slovaca 69 (4) (2019) 871-890] (where rough weighted statistical convergence for double sequences is discussed over norm linear spaces) and introduce the notion of rough weighted I2-convergence over θ-metric spaces. Also we exercise the behavior of weighted I2-cluster points set over θ-metric spaces. Based on the new notion we vividly discuss some important results and perceive how the existing results are vacillating