You could skip taking beer with.....nah, I'd rather be overloaded.
If you don't use the oven, that would be a good idea, remove it an buy an inexpensive Coleman 3-burner and use the little 1# bottles. Or get a cheap replacement burner top. If you had steel wheels I'd say change them to aluminum but it looks like you already have them. Spare tire to the front would be good for sure. Yeah, the AC is a good candidate but in NC I'd think you'd want it. Go on a diet? Change out the Labrador for a Chihuahua or get a cat instead?
You are down there already to really minimal.......gonna be tough. How much extra can the front axle take? If you don't have extra capacity up there moving weight forward won't help much.
You could move the food etc. into plastic totes and store in the rear seat area during travel.