give an inch and they'll take a mile

Make a small concession and they'll take advantage of you. For example, I told her she could borrow the car for one day and she's been gone a week—give an inch! This expression, in slightly different form, was already a proverb in John Heywood's 1546 collection, “Give him an inch and he'll take an ell,” and is so well known it is often shortened (as in the example). The use of mile dates from about 1900.