You will likely be allowed to stay for the full 6 months. Before the 6 months is up, you can apply by mail or online to extend your stay
http://www.cic.gc.ca/english/information/applications/visitor.aspIf you get married, great, you can send a spousal application. In order to qualify for common law you must live together continuously for 1 year, which is where the extending your stay thing comes into play.
Cross the border and see what happens. If you are allowed 6 weeks, or 3 months or whatever, just apply to extend your stay, then decide if marriage or common law is the way you want to proceed.
Him sponsoring you is a big commitment, he will be responsible for you for 3 years, so don't enter into it lightly, be sure its right.
Good luck!