Most legitimate church leaders would say, I think, that nobody is obligated to pay anything. You may be inspired to give money, and passing around the plate makes it easy to see who is and who isn’t giving, but the money has to come from somewhere. Most churches don’t have sufficient assets to support themselves forever.
I’m really not trying to be a smart alec here, but go to wikipedia and look up tithe. I think that will give you a pretty good background as to where passing the plate came from. When money became prevalent, it was the easiest way to donate 10 percent of your earnings to the church. I don’t think it will answer the question directly as to when it became prevalent, though.