Antoine, I just want to note that BrianLe is a Triple Crown hiker (all three of the US long north-south trails, Appalachian, Continental Divide, Pacific Crest) and has hiked a number of other long trails. So he knows whereof he speaks! I strongly urge you to pay close attention to what he says.

I have carried up to 10 days' food, but that's at only 1 pound of food per day, relying entirely on freeze-dried food and on the unfortunate fat reserves I carry. Total starting pack weight was about 28 lbs. I know that Wandering_Daisy of this forum has carried up to 14 days of food, but that was in places where she could catch fish to supplement her diet nearly every day.

You mention that there are some supermarkets along your route. There is therefore road access at those points, where, if you don't want supermarket food, you can arrange (hopefully with local residents) to cache food supplies.

Even with no weight reduction in food or gear, if you could set up one cache at about midpoint of your hike, your starting load will be about 45-50 lbs. (which all of us here consider heavy!) instead of the potentially crippling 75-80 (including the heavier pack). Your hike will have much better chances of success, and certainly will be far more enjoyable!