The most important ancient discussion of affability, despite its brevity, is Aristotle's, because it is one of the eleven virtues Aristotle explicitly examines in the Nicomachean Ethics. People have often remarked that Aristotle mixes very important virtues with relatively minor ones, but I think we should be wary of assuming that Aristotle himself thought he was doing that. If we look at the eleven virtues -- military fortitude, temperance, liberality, magnificence, magnanimity, honorable ambition, mildness, affability, truthfulness, eutrapelia, justice -- all of them are actually quite important, practically speaking, for making civic life run smoothly. Take one of the supposed lesser virtues in the list, eutrapelia, which is for Aristotle something like a consistent habit of wittiness. This may not be important by abstract moral standards, or essential for salvation of the soul, but one has only to experience (what everyone has experienced at some point) just how much a boorish or a frivolous person can ruin one's day in order to appreciate the importance of it for social relations. And in many ways the whole Nicomachean Ethics is profoundly concerned with the requirements for civic friendship, the sort of mutual well-wishing that binds a city together. It's not surprising, then, if Aristotle thinks all of these eleven are important. Moreover, in a book where civic friendship is treated as being of crucial importance, can the virtue of friendliness, dealing with the kind of outward behavior appropriate to friendship, really be treated as a 'lesser virtue'?
Aristotle locates affability as a virtue dealing with interaction in words and deed, one of the three. Of these three, one concerns truth and the other two concern pleasantness. Eutrapelia or wittiness is the virtue of pleasantness of word and deed in matters of amusement specifically, while affability is the virtue of pleasantness of word and deed in the ordinary actions of life (Nic. Eth. II.vii; cf. also IV.vi):
With regard to the remaining kind of pleasantness, that which is exhibited in life in general, the man who is pleasant in the right way is friendly and the mean is friendliness, while the man who exceeds is an obsequious person if he has no end in view, a flatterer if he is aiming at his own advantage, and the man who falls short and is unpleasant in all circumstances is a quarrelsome and surly sort of person.
So here we see that affability is a mean between a vice of excess (obsequiousness or flattery) and a vice of defect (quarrelsomeness or surliness). The first goes to ridiculous extremes to avoid giving any pain, while the latter sort of person is always opposing things for no good reason. The mean between the two is to endure or oppose things appropriately, and Aristotle says there is no name for it, but it is closest to friendship in nature, so thence arises the name philia. However, it is not friendship as such, because it does not include anything about internal affection; you can be friendly to people you dislike. The affable person is someone who will join in pleasures or not depending on the consequences and honorableness of the pleasures; whereas the flatterer is always eager to join in pleasant activities and the surly person is always disapproving of them.
Following Aristotle, Aquinas takes the virtue of affabilitas or amicitia to be a virtue, the mean between flattery, adulatio, and quarrelsomeness, litigium. The use of the term affabilitas in this context seems to come from Sirach 4:7, "Make yourself affable to the congregation of the poor" (see ST 2-2.114.1 sed contra). It is the virtue concerned with the appropriateness or becomingness of order in mutual relations. It is not complete friendship, but simply similar to friendship in that it leads one to act in a pleasant and appropriate way to those around one. It is a potential part of justice, which means that it is similar to justice in the strict sense without actually being justice in the strict sense; and thus it can be considered part of justice in a broad sense of the term. Like many of the potential parts of justice, it differs from justice by involving moral debt rather than legal debt, which is to say, that it operates not according to any strict principles of equality but according to a general sense of ongoing expectation. Moral debts, unlike legal debts, can never strictly be repaid; they are things that we owe in a vague and ongoing way to our fellow human beings. The particular moral debt here is that we owe it to our fellow citizens and human beings to behave pleasantly with those with whom we dwell, unless necessity requires us to act unpleasantly.
Aquinas compares this virtue to truthfulness. We owe it to our fellow human beings to be truthful, because without truthfulness, society must fail; but society will fail without delight, as well, and thus we have a responsibility to live in such a way that we generally delight those around us whenever we are not obligated to act in some other way. In practice, this means that we should act pleasantly toward other people in order to make their lives better, either by consoling them or encouraging them in good things, and only do things that might sadden or pain them if it would genuinely be bad for them.
Of the two opposing vices, adulation or flattery is of course the one that is more similar to affability; from this it follows both less grievous than litigium, if only considered in itself, but in practice we often flatter through deception, which makes it more serious. Neither adulation nor quarrelsomeness are in general associated with acts that are mortal sins; they may rise to become such due to the seriousness of circumstances, but in themselves they tend to be venial. While Aquinas himself does not take this step, one can see that this is precisely why affability, apparently so important to Aristotle, and a significant enough potential part of justice to be explicitly discussed in three questions by Aquinas, comes to be considered a minor virtue: its vices tend toward very petty actions, sometimes almost laughably so. And in the modern period, it will largely be confined to discussions of social graces. If we think of our experiences, however, I think we can see that affability does a lot with very little. As Aquinas says, a functioning society requires a little ordinary delight as much as it requires anything else, and almost nothing makes life run so smoothly as people in the habit of behaving in friendly ways. Perhaps a good exercise would be to go through a week noting explicitly all the ways in which people doing this make your life much better, for all that they are usually doing very minor things; after such an exercise, I think the only reasonable conclusion is to say that Aristotle was right that this is a major civic virtue and that Aquinas was right that it is necessary for the very existence of civilized life.