In the end, did the Crusades weaken or strengthen the power the Church had in European society? Why?
There are at least two major ways in which the Crusades helped increase the power that the Church had. One of these ways was psychological and one was more tangible.
The psychological impact came from an increase in the prestige of the pope. The pope came to be seen as the person at the head of the Church, defending Christianity from the Muslims. In this way, the Church gained strength because people felt that it was leading all of Europe in this huge undertaking. Europeans coalesced behind the Church's leadership in ways similar to how people fall in line behind their leaders in times of war.
The more tangible impact of the Crusades was that it made the Church richer. Kings and nobles leading their men on Crusades typically needed loans. The Church was the major source of these loans. This made a great deal of money for the Church.
In these ways, the Church gained power from the Crusades both in terms of what people thought of it and in terms of how much wealth it had.