If you want to go for the citizenship, maybe they will check things like whether you pay taxes, or utility bills...I haven't gone that far, so I am not sure how exactly they will ask us to prove. But my hobby & I go to the States about twice a week & we don't have any problem so far, except once. We usually buy groceries in the States so we show them the receipts if they ask us to. But the other day we didn't buy any groceries so I told them we just had a lunch & didn't buy anything. The lady asked us to pull up the car to have a check. They searched the car very carefully & let us go later because they didn't find anything. BTW, we drive a canadian registered car & live in the border city.