There is one late writer, David Hume, Esq. who, it must be confessed, hath excelled all that went before him in an extraordinary account of the nature of virtue. I have taken no notice above of his principles, if they may be called so, because I think both him and them worthy of the highest contempt; and would have disdain'd to have made mention of his name, but that it affords me an opportunity of expressing my sense of the wrong measures taken by many worthy and able men, who, in sermons and other discourses, give grave and serious answers to his writings.
In essence, Witherspoon thinks Hume's moral theory reduces itself to absurdity:
As to himself, that man must be beyond the reach of conviction by reasoning, who is capable of such an insult upon reason itself, and human nature, as to rank all natural advantages, mental and corporeal, among the virtues, and their contraries among the vices. Thus he hath expressly named wit, genius, health, cleanliness, taper legs, and broad shoulders among his virtues; diseases he also makes vices; and consistently enough, indeed, takes notice of the infectious nature of some diseases, which, I suppose, he reckons an aggravation of the crime.
This is an often-overlooked feature of Hume's account of virtues, which assigns virtues in terms of both immediate pleasure and utility. He discusses wit, genius, and cleanliness in 3.3.4 as natural abilities, but also denies that there is a clear distinction between natural abilities and natural virtues. He explicitly lists "[b]road shoulders, a lank belly, firm joints, taper legs" as natural virtues for men in Treatise 3.3.5, and also mentions "an air of health" in the same way (with "a sickly air" as its opposite). Witherspoon is arguably not being fair on the infection point; the disease that Hume mentions as infectious (in a completely different part of the Treatise) is "the itch" -- that is, scabies. On the other hand, the reason Hume gives for our being ashamed of such diseases is that they "are either dangerous or disagreeable" to the people who have them (Treatise 2.1.9), which could be read as putting it in a category of natural vice, on Hume's account of how vice is to be understood.
Witherspoon takes this all to be obviously absurd, and continues:
And, as to mankind in general, if they were at that pass as to need a refutation of such nonsense, as well as impiety, it would be in vain to reason with them at all. If I were to contrive an answer to this writer, it would be a visible, instead of a legible answer: it would be to employ a painter to make a portrait of him from the life; to encompass him with a few hieroglyphics, which it would not be difficult to devise; to inscribe upon his breast these words, HEALTH, CLEANLINESS, and BROAD SHOULDERS; and put the following sentence in his mouth, which he hath adopted from a French author, "FEMALE INFIDELITY when it is known is a small matter, and when it is not known, is nothing." This would be very proper when applied to his writings, who, as well as his friend and coadjutor without a name, makes "our most important reasonings upon many subjects to rest ultimately upon sense and feeling."
The "friend and coadjutor without a name" is Henry Home, Lord Kames, and the quotation is from Essays on the Principles of Morality and Natural Religion, which itself criticizes Hume's Treatise extensively (although Home was indeed Hume's friend). Witherspoon is primarily satirizing the notion of immortalizing a person for their health, cleanliness, and broad shoulders, but there may be a sharper bite here, as well, if one thinks of this in terms of this engraving of Hume, which Witherspoon possibly could have seen (I believe it is found in the History in 1754; the essay on justification was first published in 1756):
Imagine 'Health, Cleanliness, Broad Shoulders' blazoned as a eulogy on that.
The French author is La Fontaine; Hume quotes it in "A Dialogue" as part of a broader notion that female chastity is treated as a virtue because it is taken to have public utility. Hume's position is arguably more sophisticated than is attributed to him, on this topic, at least, but if you look at criticisms by other people of Hume's account of morals, this exact point is a common objection, and Witherspoon is very far from being the only person pitched to sarcasm by it.
Witherspoon ends the footnote by dismissing people who think he should be nicer about a matter like this.
It is probable some over delicate persons will think this is not treating him with sufficient decency; but till there be a plan agreed upon, of the measures of decency due from infidels to Christians, and from Christians to infidels, whether he does not deserve far worse treatment from any who believes the gospel, I leave to the judgment of those who will read his writings.
This is not the only place that this criticism of Hume comes up; he mentions it again, with less sarcasm but more dismissal, in his moral philosophy lectures, and a couple of other places, but this is the passage where he develops the point most.