You will find that in most parks that give you a weekly rate, that rate is really not discounted that much if they also give Good Sams, military, AAA or other 10% discounts. Weekly rates are usually pay for six days and get the seventh free but they will not let you use the Good Sam rates for the six nights. So if the park charges $30/night, you get seven nights for $180. If you paid for seven nights at the Good Sams rates it would be $210 - $21 or $189, so you save a whopping $9 by staying another night. That is not a significant enough savings to make me stay an extra night if I would rather be down the road somewhere.
That said, some parks will give you the 10% discount on the weekly rate as well if you qualify. The only way to know is to ask them, don't assume.