Weighted bilinear identities and supercongruences for Apéry-like polynomials

We establish weighted bilinear summation identities for two families of Apéry-like polynomials $g_n(x)$ and $v_n(x)$. The identities express weighted sums in terms of consecutive endpoint values and, when necessary, lower moments. For $g_n(x)^2$ we obtain identities with weights $(2n+1)^r$ for $1\le