Alabama here! DD4, DH & I budget $110/week for groceries plus $50/week for eating out. While we don't always hit that $110, I leave that as our budgeted amount because on a week meat or chicken is on sale, I will stock up and may go over my $110, but will stay under my MONTHLY budgeted amount (we keep our finances monthly instead of broken down per week).
1) Coupon like a mad woman- google name of product (example: 'yoplait') and 'coupon' and see if you get any hits for printable yoplait coupons (or whatever product you are looking for). Personally, I am a member of hotcouponworld dot com and they are a great bunch of folks. There is a board for almost every store out there (Target, Wal-Mart, K-Mart, Winn Dixie, CVS to name a few), and folks will talk about the deals they got, and what coupons they used, and how they got their coupons. This site is also used to trade coupons that you CAN'T use with someone who CAN use them, and in return get coupons that you CAN use.
2) Collect coupons from family members! If there's a printable coupon that is a super deal, since each computer can only print 2, I request that my mother, father, and father-in-law each print this coupon 2x so I will end up with 8 coupons for the item. Also, my father and father-in-law both get home delivery of the paper and they don't use their coupon inserts- they throw them away (I know, makes you want to cry, right? Me too!). I have asked that they save them and send them to me when possible. My father mails his weekly on Monday morning after spending Sunday afternoon clipping, and then my father-in-law, who lives closer, collects them until we get together once a month. Also, my neighbor gets home delivery of the paper and does not use his coupons- he said I am more than welcome to take them from his paper every Sunday if I'd like. Ask around- there are people out there that get the paper and don't use what comes in it!
2) Gift Cards for Prescriptions. Might sound a little crazy, but I know that we have a CVS, Rite Aid, Walgreens, Target, and Publix that have all put prescription coupons in their inserts in the last month or so. Either when you bring a new prescription to them to get filled, or transfer a prescription from one store to their store, they will reward you with a gift card (if you have the coupon from their weekly ad). At Christmas, I got 2 from Rite Aid for $30 each- this is how I did much of the Christmas shopping for my family. More recently, I've gotten a $10 Target & plan to get a $30 Publix gift card soon- you can use these gift cards, even at pharmacies, to stock up on grocery items, since these gift cards are like 'free money' anyways! That would help your budget for that month a LITTLE...
Just a few ideas. Enjoy & Happy Shopping!