I am sorry to hear that your fellow is lethargic, has lost weight, has been vomiting after eating, sneezing at night, has labored breathing, and is now not eating.
His sneezing at night may be secondary to reflux (passive back flow of stomach acid into his esophagus and back of his throat/nose) irritating his nasal passages. Likewise the eye discharge could be secondary to that reflux, and poor nutrition from vomiting and weight loss.
Labored breathing could be due to secondary aspiration pneumonia (breathing stomach acid/contents into his lungs when reflux occurs), primary heart or lung disease, or metastatic cancer that has invaded his lungs.
His low thyroid levels at the time of his vaccines could indicate a slow, chronic disease process that had not yet become apparent when he was vaccinated, but was an issue even then. This includes early organ failure, a chronic infection or cancer.
Given his weight loss everywhere but his abdomen it is possible that he has an abdominal mass that has spread to his lungs, is putting pressure on his gastrointestinal tract causing reflux and vomiting and increasing caloric needs for growth, thus his rapid weight loss. This mass likely would have been present 6 weeks ago, but difficult to palpate in such a big dog that was also overweight.
Of course without testing I cannot tell you for sure what is going on with him, but I would be highly suspicious of:
1) organ failure (kidney or liver disease), or ketoacidotic diabetes can lead to a build up of metabolic wastes that lead to nausea, and a loss in appetite and an inability to process the nutrients he does take in all of which leads to lethargy and weight loss as well as vomiting and diarrhea.
2) A gastrointestinal foreign body, or an abdominal mass/tumor placing pressure on his gastrointestinal tract can lead to loss of appetite because he feels full. Over time that leads to weight loss. If he isn't eating normally and is vomiting he will feel weak.
3) Systemic infections can cause a build up of toxins from the infection will cause a decrease in appetite and lead to vomiting and diarrhea.
4) Inflammatory bowel disease causes an inability to digest and absorb food, and the inflammation affects appetite. This can also lead to fluid accumulating in his abdomen, but things rarely progress this quickly with IBD.
Your fellow needs to see a veterinarian for a rcheck examination, complete blood count, biochemistry profile and urinalysis to start. But with many cancers bloodwork and routine radiographs may not be diagnostic. In those cases an abdominal ultrasound can be helpful.
In the meantime at home to try to decrease possible nausea and improve his appetite you can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These are acid reducers, are very safe, and may help her feel better. They can be used as needed.
You can also try a bland diet with increased fluids to perk her appetite and get her better hydrated. A homemade diet for this is 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats and juices drained off the meat, and 2/3 boiled, plain white rice. Add low salt beef or chicken broth to the meals as well to improve palatability and get more fluids in which should help as well.
In an older fellow with these sorts of symptoms it is likely she has some sort of serious disease process going on if she isn't bouncing back with simple supportive care. He likely needs diagnostic testing to evaluate him, but at least you can start with these things.
Best of luck with your fellow, please let me know if you have any further questions.