I have sometimes thought it very odd that Venice would want to sack Constantinople, seeing how the two were Christian (albeit Latin vs. Byzantine derivations) and how the former liked to associated itself with the traditions of the latter. The sack, which occurred in 1204 during the Fourth Crusade, has had ramifications down the ages; in the last few decades, Pope John Paul II apologized to some of the Eastern patriarchs for the sacking of the city (and presumably for the brutality of the Crusaders toward the city and its citizens), meaning it was not an event easily forgotten. I have been doing some reading on Venetian history
and so far, this is what I have come up with in terms of why the sack occurred.
1) The French crusaders drastically overestimated the size of its crusading army
(by 2/3), and therefore hired the Venetians to produce a fleet which was far too large and expensive for anything the French ended up using. Because of this, France faced the dilemma of how to pay its bill. The subsequent arrangement made was that Venice would receive a portion of any income taken as war booty, thereby opening up the doors for the two nations to want to go "warring" for income.
2) The conquest of Zara
: Along the eastern coast of the Adriatic lay the Christian city of Zara (Zadar, Croatia), an upstart city which was starting to compete with Venice. Venice, which sought to be the lone superpower on the eastern Mediterranean, wanted to take out Zara at that point in time. While this is not something the French were normally accustomed to doing, they complied, perhaps out of feelings of economic obligations to Venice. The income derived from this conquest must have been enticing to both parties, and probably caused their eyes to be cast on larger and more lucrative prizes, such as Constantinople (rather than to the Holy Land).
3) French political aspirations
: Building up to this time were some members of French royal society that wanted to replace the Byzantine emperor with one more in line with French ideals, or at least more friendly to the French on account of blood relations. Although this plan may have been known by the Venetians, this was something that seems to have been hatched up in French minds, rather than Venetian ones.
4) General resentment toward the Byzantine Empire
: In 1171 the Byzantines had seized lands owned by Latins. This would obviously have ruffled some feathers in Venice as something unwelcome and possibly even illegal, and it would likely have been remembered three decades later. Adding to this was the way the Byzantines started conducting business with Venice and Venice's rival cities (Genoa, Pisa). Although this is a bit hazy, it seems that Constantinople was playing politics by "stringing Venice along" one moment, then giving an advantage to her rival cities the next. This would not have been to Venice's liking as the city was trying to assert commercial superiority in the Adriatic and eastern Mediterranean at this time.
All of these factors were at play when the Venetians and French made the decision to go to Constantinople rather than the Holy Land after they sacked Zara. This was no small feat entering Constantinople, which was a city well-defended (water on three sides). Once they made it into the city, the pillaging began.