Objection 1. It seems that covetousness is not a spiritual sin. For spiritual sins seem to regard spiritual goods. But the matter of covetousness is bodily goods, namely, external riches. Therefore covetousness is not a spiritual sin.
Objection 2. Further, spiritual sin is condivided with sin of the flesh. Now covetousness is seemingly a sin of the flesh, for it results from the corruption of the flesh, as instanced in old people who, through corruption of carnal nature, fall into covetousness. Therefore covetousness is not a spiritual sin.
Objection 3. Further, a sin of the flesh is one by which man's body is disordered, according to the saying of the Apostle (1 Corinthians 6:18), "He that committeth fornication sinneth against his own body." Now covetousness disturbs man even in his body; wherefore Chrysostom (Hom. xxix in Matth.) compares the covetous man to the man who was possessed by the devil (Mark 5) and was troubled in body. Therefore covetousness seems not to be a spiritual sin.
On the contrary, Gregory (Moral. xxxi) numbers covetousness among spiritual vices.
I answer that, Sins are seated chiefly in the affections: and all the affections or passions of the soul have their term in pleasure and sorrow, according to the Philosopher (Ethic. ii, 5). Now some pleasures are carnal and some spiritual. Carnal pleasures are those which are consummated in the carnal senses--for instance, the pleasures of the table and sexual pleasures: while spiritual pleasures are those which are consummated in the mere apprehension of the soul. Accordingly, sins of the flesh are those which are consummated in carnal pleasures, while spiritual sins are consummated in pleasures of the spirit without pleasure of the flesh. Such is covetousness: for the covetous man takes pleasure in the consideration of himself as a possessor of riches. Therefore covetousness is a spiritual sin.
Reply to Objection 1. Covetousness with regard to a bodily object seeks the pleasure, not of the body but only of the soul, forasmuch as a man takes pleasure in the fact that he possesses riches: wherefore it is not a sin of the flesh. Nevertheless by reason of its object it is a mean between purely spiritual sins, which seek spiritual pleasure in respect of spiritual objects (thus pride is about excellence), and purely carnal sins, which seek a purely bodily pleasure in respect of a bodily object.
Reply to Objection 2. Movement takes its species from the term "whereto" and not from the term "wherefrom." Hence a vice of the flesh is so called from its tending to a pleasure of the flesh, and not from its originating in some defect of the flesh.
Reply to Objection 3. Chrysostom compares a covetous man to the man who was possessed by the devil, not that the former is troubled in the flesh in the same way as the latter, but by way of contrast, since while the possessed man, of whom we read in Mark 5, stripped himself, the covetous man loads himself with an excess of riches.
Source: Summa Theologica (New Advent)