Weakly marginal subgroup

For a single word-letter pair
Suppose $$w$$ is a word in letters $$x_1,x_2,\dots,x_n$$ and $$x_1$$ is a letter of $$w$$ (we can take the letter to be $$x_1$$ without loss of generality). The weakly marginal subgroup of a group $$G$$ corresponding to $$w$$ and $$x_1$$ is the subgroup:

$$\{ g \in G \mid w(gx_1,x_2,\dots,x_n) = w(x_1,x_2,\dots,x_n) = w(x_1g,x_2,\dots,x_n) \ \forall \ x_1,x_2,\dots,x_n \in G \}$$

For a collection of many words and chosen letters in each
The weakly marginal subgroup corresponding to a collection of word-letter pairs is defined as the intersection of the weakly marginal subgroups corresponding to each word-letter pair.

Examples
Most of the examples are common with marginal subgroup. In addition, we have some other examples, such as centralizer of derived subgroup, which is weakly marginal but not necessarily marginal.