Hi pacer,
Arguments that contain examples supporting a given position, or else counterexamples refuting a conflicting position, should be evaluated in the same way as any other argument. Does the premise/s (containing an example) support the given conclusion? To weaken the argument, you want to show that the example is an exceptional case that is not illustrative of the (typically) broader conclusion argued by the author. This is typically how we weaken inductive arguments. To strengthen such arguments, you do the opposite. For instance:
Some may argue that getting in to Yale Law is exceptionally difficult, but this is obviously not the case. Just look at Mary: an average student at a community college whose LSAT score was a mere 159. And yet, she will be a 1L at Yale Law next year!
How do you weaken this argument? By showing that the counterexample using Mary is somehow exceptional and not indicative of the norm. Maybe Mary is also a Pulitzer-prize winner, or an Olympic gold medalist. Or, maybe Mary is truly unremarkable - a confused pre-law trying to figure out what to do with her life. The relevance of this counterexample will determine the validity of the argument at hand.
Does this make sense? Let me know.
Thanks!