This is getting absurd... (Chelsea)

 What? Did you not read her post?

For chews, check your feed store, if you have one locally.  I buy a pretty large bag of mixed chews that contains moo tubes, bully sticks, those creepy pig nose things, etc for about $12. It varies with each bag, but most times it's full of bully sticks. I feed several chews daily with my crew (Grimmy needs things to chew on lest he find things he shouldn't) , and the bag still lasts several weeks. (and that's with four dogs)

That's the tough part of overnutrition. Protein and fat not used get stored as fat. So, the carb filler might help. It's odd that the vet didn't find a metabolic problem. Anyway, good luck.

 This is the part I don't understand - surely the carbs get released slowly, meaning they are more likely to be stored as fat?  I didn't think pet dogs needed many carbs?   Argh!  Nutrition confuses me!

 I would NEVER cut out omega fatty acids.  For the most part they are high in UNSATURATED fats , GOOD fats , not the kind that add to weight gain. However.... EXTRA VIRGIN COCONUT OIL actually encourages weight loss. You might consider substituting that for one meal a day.  

http://www.organicfacts.net/organic-oils/organic-coconut-oil/health-benefits-of-coconut-oil.html

 Another thing to consider is that your dog might need more PROBIOTICS. If there's a digestion problem and the dog is not able to appropriately utilize the nutrients from the food, that can cause weight gain. You might also consider DETOXING your dog  with a homeopathic detox ( Newton's or similar products found online or at your local healthfood store ).  

 Adding unfiltered apple cider vinegar will also help with detoxing but is beneficial for digestion, tartar/plaque prevention, stone/crystal formation prevention, balancing pH and improving coat and skin as well as weight control and maintenance.

http://www.gomestic.com/Pets/Ten-Good-Reasons-to-Give-Your-Pet-Apple-Cider-Vinegar.30311

 I'm not endorsing the product below... just giving an example of a Detox program for pets

Hope this info is helpful for you.