It's a common trope in fiction, but from what little I've read, it doesn't seem to be something the Church has been very keen on. I doubt it never happened (there were a lot of priests and plenty of people who justified their violent actions through religion), but that's just conjecture, not facts. I have heard Eastern Orthodox priests are more willing to bless weapons or just about anything else.
Sorry if I'm light on specifics as to what era, but if I knew all the facts, I wouldn't be asking.
The catholic church (at least in the Middle Ages, I don't know what's up in more recent centuries) certainly did bless both weapons (and other objects).
Rivard features such a blessing from the 12th century pontifical of Besançon:
God, who constituted three orders of men in the whole world after the fall of Adam, by means of which your faithful people may remain quiet, secure and free from all the violence of evil, be present by our supplications and make use of this sword, which we bless by the invocation of your name [...] so that he may both repress the enemies of the church of God laying snares and powerfully defend himself by means of your protection from all the fraud of the enemy.
But a more mainstream one is this (in his translation):
Hearken to our prayers we entreat, Lord, and may you deign by the right hand of your majesty to bless this sword, with which this your servant N. desires to be girded about, in so far it can be the defense and protection of churches, widows, orphans and all those serving God, against the ferocity of the pagans, and may it be dread, terror and fear for others laying snares.
Which is the blessing in Ordo 244 from the Pontificale Romano-Germanicum (PRG) a widely spread and important pontifical in the Middle Ages, and indeed basis for later Roman liturgy. In other words the blessing of swords by this rite was a standard and approved practice. A version different in only a few words is Durandus' (in Andrieu, XXVIII De benedictione novi militis, p447-50), which adds a whole coronation-like ceremony where the sword is presented to the knight, who swears fealty to god and the kings of France (obviously in non-French texts that'd change) and then prays for strength from god in defending the faith et cetera, and brandishes the sword three times before wiping the blade and putting it in the scabbard. There was a whole ritual about it which was likely centuries old by the time Durandus wrote down his version and similar ceremonies would be carried out for centuries to come.
For instance, here's the page (with images) 'on the blessing of arms' (De benedictione armorum) in the Pontifical of Clement VIII, published in 1595. (with swords and banners of war on the following pages)
Should it need pointing out though, there are clear stipulations here of the chivalrous purposes for which the weapons are blessed. It didn't amount to a general blessing of weapons or violence for any purposes. (on the other hand it wouldn't be out of character for a medieval person to assume such a blessing gave inherent power to the weapon regardless of circumstance; a lot of contemporary magic was often based on that kind of assumption)
Sources:
Michel Andrieu (ed), Le pontifical Romain au moyen-âge, vol. 3: Le Pontifical de Guillaume Durand, Biblioteca Apostolica Vaticana, 1940
Cyrille Vogel and Reihard Elze, La pontifical romano-germanique du dixième siècle, 2 vol, Studi e Testi, Biblioteca Apostolica Vaticana, 1963
Derek A. Rivard, Blessing the World: Ritual and Lay Piety in Medieval Religion, Catholic University of America Press, 2009