 We consider \alpha=}   2W , 4W , 6W, where W is the maximum edge weight in G. We first show that every n-node graph has a subsetwise 2W-spanner on O(n |S|^{1/2) edges where S \subseteq V and W is a constant.
<meaning-changed>  We consider \alpha=}   2W , 4W , 6W, where W is the maximum edge weight in G. We first show that every n-node graph has a subsetwise 2W-spanner on O(n |S|^{1/2) edges where S \subseteq V and W is a constant.
 We consider \alpha=} error. These extensions are not immediate, due to a key lemma about the size of shortest path neighborhoods that fails for weighted graphs. Despite this, we recover a suitable amortized version, which lets us prove direct extensions of classic +2 and +4 unweighted spanners (both all-pairs and pairwise) to + 2W , 4W , 6W, where W is the maximum edge weight in G. We first show that every n-node graph has a subsetwise 2W-spanner on O(n |S|^{1/2) edges where S \subseteq V and W is a constant.