Looks like a pretty nice camper. If your going to be overweight, it isn't going to be by much. You can either consider your payload sticker the code or in the words of infamous Captain Jack Sparrow "...the code is more what you'd call "guidelines" than actual rules." Yes, do your best to be within target but don't freak out if your just a bit over.
If your dead set on this camper then you got a few options still available...
1. As others already mentioned, if you plan on boon-docking a lot and your not in the South see if you can ditch the AC. You would need a generator or 120v anyway to run it. Maybe you could get a skylight put in it's place?
2. Don't drive with your water tanks full until you get close to your destination.
3. Consider purchasing a water filter system so you can use local sources when camping.
4. Planning on sticking close to civilization? Leave the spare tire, jack and tire tools at home. Yup, might be taking a risk but a good set of tires in good condition will treat you well.
5. Get a lighter dog... (okay, maybe not such a great suggestion)
6. Lose some weight... (okay, maybe not as easily said then done)
7. Look up "Ultralight Backpacking" and purchase that type of gear for your camping adventures. These backpackers can live out in the wilderness for 5 to 7 days on 20 to 30lbs of food and gear.
Some of these steps are more extreme than others and may or may not be advisable but they will help to keep the weight police off your back. That being said, all things being equal, I think if you exceeded your Gross Vehicle Weight by a 100lb to 200lb you will be just fine.
1999 F350 Dually with 7.3 Diesel
2000 Bigfoot 10.6 Camper