We revisit the Weighted Shortest Common Supersequence (WSCS) problem, that is, the SCS problem on weighted strings, that was introduced by Amir et al. [SPIRE 2011]. A weighted string, also known as a Position Weight Matrix (PWM), is a sequence of probability distributions over the alphabet. In the WSCS problem we are given two weighted strings $W_1$ and $W_2$ and a threshold $1/z$ on probability and are to compute the shortest (standard) string $S$ such that each of $W_1$, $W_2$ matches a subsequence of $S$ (not necessarily the same) with probability at least $1/z$. Amir et al. showed that a log-probability version of this problem is NP-complete. We present an algorithm that solves the WSCS problem for two weighted strings of length $n$ and over a constant-sized alphabet in $O(n^2\sqrt{z} \log{z})$ time. This matches conditional lower bounds since it is known that WSCS cannot be solved in $O(n^{2-\varepsilon})$ or $O^*(z^{0.5-\varepsilon})$ time unless there is a breakthrough improving upon long-standing upper bounds for fundamental NP-hard problems (CNF-SAT and Subset Sum, respectively). We also discover a fundamental difference between the WSCS problem and the Weighted Longest Common Subsequence (WLCS) problem that was introduced by Amir et al. [JDA 2010] by showing that WLCS cannot be solved in $n^{O(1)} f(z)$ time, for any function $f(z)$, unless $P=NP$.