Objection 1. It would seem that the weeping of the damned will be corporeal. For a gloss on Luke 13:28, "There will be weeping," says that "the weeping with which our Lord threatens the wicked is a proof of the resurrection of the body." But this would not be the case if that weeping were merely spiritual. Therefore, etc.
Objection 2. Further, the pain of the punishment corresponds to the pleasure of the sin, according to Apocalypse 18:7: "As much as she hath glorified herself and lived in delicacies, so much torment and sorrow give ye to her." Now sinners had internal and external pleasure in their sin. Therefore they will also have external weeping.
On the contrary, Corporeal weeping results from dissolving into tears. Now there cannot be a continual dissolution from the bodies of the damned, since nothing is restored to them by food; for everything finite is consumed if something be continually taken from it. Therefore the weeping of the damned will not be corporeal.
I answer that, Two things are to be observed in corporeal weeping. One is the resolution of tears: and as to this corporeal weeping cannot be in the damned, since after the day of judgment, the movement of the first movable being being at an end, there will be neither generation, nor corruption, nor bodily alteration: and in the resolution of tears that humor needs to be generated which is shed forth in the shape of tears. Wherefore in this respect it will be impossible for corporeal weeping to be in the damned. The other thing to be observed in corporeal weeping is a certain commotion and disturbance of the head and eyes, and in this respect weeping will be possible in the damned after the resurrection: for the bodies of the damned will be tormented not only from without, but also from within, according as the body is affected at the instance of the soul's passion towards good or evil. In this sense weeping is a proof of the body's resurrection, and corresponds to the pleasure of sin, experienced by both soul and body.
This suffices for the Replies to the Objections.
Source: Summa Theologica (New Advent)