There is a pious and beautiful tradition which says that St. Peter cried each time he heard a cock crow since that reminded him of when he denied Jesus. It also says that since he heard a cock every morning, those tears etched furrows on his cheeks.
I do not really know if tears for sins can create crevices in a face, but I do know that tears for sins are an effect of contrition or compunction of heart. Compunction of heart is a disposition of the soul that keeps it in a habitual state of contrition for the sins committed.
This disposition, when it becomes a habitual state, makes the one who has fallen into mortal sin and has been raised by the mercy God not fall back into that sin again. On the other hand, without this disposition it is almost impossible not to commit that sin again. Therefore, compunction of heart should be a habitual and stable disposition. When we achieve this disposition, we are in state of hatred to sin. The interior movements that this disposition produces are every effective against temptations. St. Bernard used to say that compunction of heart is similar to perfection.
If we are inconstant and instable, if we go up and down in our spiritual life, going from good proposals and resolutions to infidelities and falls, it is probably because we have not achieved this compunction of heart yet. We should try to go to prayer with this disposition and make our prayer a compunction of heart.
“To speak much in prayer is to do a necessary thing with superfluous words. To pray much means to knock for a long time with a pious movement of the heart at the door of the One to whom we pray; and prayer consists more in groaning and weeping than in great speeches and copious words. God collects the tears shed in His presence; our groans are not ignored by the One who created everything with his Word and has no need of our human words.” (St. Augustine, Letter 130,10)
We should always ask for the grace of tears. In fact, there is an old tradition to ask for this grace. One example of a prayer to ask for that gift says: “Almighty and merciful God, who hast caused a fountain of living water to flow out of the rock for the thirsty people; cause tears of compunction to flow from our hardened hearts, that we may weep for our sins, and merit remission of our sins through thy mercy. Amen”
