A counter weight character is one who balances the extremes of a major character. An example is Enkidu as a counter weight character to Gilgamesh in The Epic of Gilgamesh. By himself, Gilgamesh is a rash, hard-driving, demanding ruler who exhausts his people and resources. Enkidu balances these things in Gilgamesh by refocusing his energy and calming him down: Enkidu counters Gilgamesh's tendencies by influencing him to move toward countering behaviors.
In The Playboy of the Western World, Widow Quin is a counter weight character to Christy. She also attempts to be a countering influence to Pegeen and the other villagers but is not successful as they never exhibit improved behaviors. Christy first tells the whole story of his father's end to Widow Quin. One of her comments is an ironic remark aimed at influencing him to take a better view of himself and not be swept away by the myth around him and the force of group mentality:
WIDOW QUIN -
Don't be letting on to be shy, a fine, gamey, treacherous lad the like of you.
Another example of Widow Quin's countering influence is her attempt to persuade Christy to accept Shawn's offer to get out of town and stay out. She does influence him in some regards, for example, to participation in the sports games, which is where he eventually gains his title of Playboy of the Western World. As a whole though, Widow Quin is not very successful in her task of influencing Christy to behave in a less excessive way. Christy's exit from the play demonstrates her failure:
CHRISTY. Go with you, is it? I will then, like a gallant captain with his heathen slave. Go on now and I'll see you from this day stewing my oatmeal and washing my spuds, for I'm master of all fights from now. (Pushing Mahon.) Go on, I'm saying. ... I'll go romancing through a romping lifetime from this hour to the dawning of the judgment day.