However, I think there is utility in attacking a weak man argument when (1) the weak man argument is widely believed or distributed and (2) when there is an acknowledgment that the defeat of the weak man argument does not settle the larger question the argument was said to address.
Both of these points are right and admit of reasoned defense, so I thought I'd briefly say something about them.
Let's think about why philosophers always insist that people focus on the strongest rather than the weakest argument (even if they do not always comply with this themselves). The reason is that attacking a weak argument is not like finding the weak point on a chain -- break the weakest link and you break the whole chain. Rather, weak arguments are arguments that do the least real work. If you want to bring down a roof or a wall or a fortress, you can't do it by sapping the supports that aren't really supports; you have to find the load-bearing supports and bring down some of those. All a position needs is one thoroughly good argument; by criticizing the strongest argument and showing that it is not enough to support the position, you both remove the position's strongest support and, a fortiori, show that it is unlikely that anything else will support it either. But there are cases where you'll want to focus on criticizing the weaker arguments, anyway; for instance, if you think they are distracting people from more serious issues.
What norms govern such a case, determining whether it is a good move or a bad move? Not logical ones, at least primarily; demolishing a weak argument does nothing to undermine the position, and while a weak argument may have logical problems, very often the weakness will lie elsewhere -- e.g., false assumptions. Rather, the primary norms here are ethical. I've noted before that arguments have two aspects: their logical structure and their rhetorical presentation. When we are looking at weaker arguments rather than stronger ones, we are very far from considering crucial arguments for the conclusion, and thus very far from considering the conclusion in itself; our only concern is basic persuasion about the arguments themselves, and this is a rhetorical matter. But rhetorical matters, while they are not strictly bound to logical standards (since persuasion does not depend wholly on logical standards), are still governed by ethical standards. Thus the attacking of a weak man can be dishonest or imprudent, unjust or incompetent; it's not actually a fallacy, just one of the things you might be doing with an argument, but like any sort of action it can be done well or badly, rightly or wrongly.
We can therefore see the underlying basis for Steven Maloney's two suggestions.
(1) If an argument is widespread, it might indeed be reasonable to attack it rather than stronger arguments, if you are primarily concerned with eliminating that argument from the discussion (precisely because it is such a weak argument).
(2) But the weaker arguments are not load-bearing; that is, the positions for which they argue do not depend on them, and therefore attacking these weaker arguments does little to nothing to harm the position itself. It would be intellectually dishonest to suggest otherwise, and therefore we can reasonably expect people who chose to attack the weaker arguments because they are more widespread to acknowledge the fact that they are weaker and that their criticisms of these arguments do nothing to address the larger question.
