I remember being offended by this the first time I read it. It seemed to be advising dishonesty and trickery.
When you see a person weeping in sorrow either when a child goes abroad or when he is dead, or when the man has lost his property, take care that the appearance do not hurry you away with it, as if he were suffering in external things. But straightway make a distinction in your own mind, and be in readiness to say, it is not that which has happened that afflicts this man, for it does not afflict another, but it is the opinion about this thing which afflicts the man.
This covers similar ground to earlier sections, and echos part 5: "Men are disturbed not by the things which happen, but by the opinions about the things". In this case though, it is in the context of other people's problems. To avoid getting pulled into another's grief, we should see the grief as it is: an opinion.
So far as words then do not be unwilling to show him sympathy, and even if it happens so, to lament with him. But take care that you do not lament internally also.
This is the part I found initially confronting. Feigning sympathy seems pretty distasteful. But I think it can be read another way. You should support a friend in their grief, but not lose yourself to it. In fact, by maintaining your Stoic reason, you may be more use to them than if you joined them in their grief.