Well I don't think it was jealousy, byzantium was not looked upon in a good light by this time, the original crusade was called in order to help reclaim their land from Seljuk Turks however in the end the leader of byzantium never arrived with his men to help the crusaders in their battle as he had turned back thinking they were going to loose and planning to leave them for dead, this led the crusaders to feel they should keep the land they had fought for themselves and from that point led on to distrust. At times byzantium even worked against the crusaders and during the second crusade they were even suspected of double crossing the western knights. The reality is that the call for help was a calculated way of using religion to get an army of westerners to fight for Constantinople for free but it ended up backfiring massively. The claims that the crusaders were carrying out slaughter is also one sided as they would have never been there in the first place of the Seljuk Turks were not invading and slaughtering in the byzantium lands.

​@@wendyHew "The Latin soldiery subjected the greatest city in Europe to an indescribable sack. For three days they murdered, raped, looted and destroyed on a scale which even the ancient Vandals and Goths would have found unbelievable. Constantinople had become a veritable museum of ancient and Byzantine art, an emporium of such incredible wealth that the Latins were astounded at the riches they found. Though the Venetians had an appreciation for the art which they discovered (they were themselves semi-Byzantines) and saved much of it, the French and others destroyed indiscriminately, halting to refresh themselves with wine, violation of nuns, and murder of Orthodox clerics. The Crusaders vented their hatred for the Greeks most spectacularly in the desecration of the greatest Church in Christendom. They smashed the silver iconostasis, the icons and the holy books of Hagia Sophia, and seated upon the patriarchal throne a whore who sang coarse songs as they drank wine from the Church's holy vessels. The estrangement of East and West, which had proceeded over the centuries, culminated in the horrible massacre that accompanied the conquest of Constantinople. The Greeks were convinced that even the Turks, had they taken the city, would not have been as cruel as the Latin Christians. The defeat of Byzantium, already in a state of decline, accelerated political degeneration so that the Byzantines eventually became an easy prey to the Turks. The Fourth Crusade and the crusading movement generally thus resulted, ultimately, in the victory of Islam, a result which was of course the exact opposite of its original intention." Speros Vryonis, "Byzantium and Europe"