Divisibility properties of weighted $k$ regular partitions

We study a generalized class of weighted $k$-regular partitions defined by $$\sum _{n=0}^{\mathrm{\infty }}{c}_{k,r_1,r_2}(n)q^n=\prod _{n=1}^{\mathrm{\infty }}\frac{(1-q^{nk}{)}^{r_1}}{(1-q^n{)}^{r_2}},$$ which extends the classical $k$-regular partition function $b_k(n)$. We establish new infinite families of Ramanujan-type congruences, divisibility results, and positive-density prime sets for which $c_{k,r_1,r_2}(n)$ vanishes modulo a given prime.