I am very, very concerned about your fellow.
Most amphibians secrete a horrible tasting mucous and thus lead to drooling, foamy secretions as the mucous mixes with air, and possibly vomiting should a dog bite or mouth them. He would need to actually mouth the frog to get those symptoms. That effect should not last long however, and I would not expect weight loss with this.
There are only 2 truly toxic toad species in the United States.
One is the Colorado River toad, found in northern Mexico and the southwestern United States.
The other toxic species is the Marine or Cane toad found in Florida or the very Southeastern part of the US.
Symptoms of exposure to these toads generally occur within minutes and include drooling, pawing at the mouth, vocalization, red, inflamed gums and tongue or very pale gums, difficulty breathing, incoordination, seizures, a high body temperature and complete collapse.
Since he is still alive it is very unlikely that he came into contact with one of those.
He likely isn't having diarrhea because he doesn't have anything to pass because he isn't eating.
So the question is why is he drooling so much and so extremely nauseous (he likely is nauseous because he is drooling and not eating), losing weight and very, very thirsty.
Drooling can be a sign of nausea but it can also be a sign of oral pain due to an infected tooth or a foreign body caught between his teeth, on the roof of his mouth or in the back of his throat. Sometimes it is a sign of an oral tumor. Organ failure is possible as well.
It can also be due to a nerve problem that is making it difficult for him to control his tongue or close his mouth properly. Since he is drinking without any trouble I believe that is less likely.
Finally it can also be a response to eating a bitter bug or plant piece. If it comes along with facial swelling or hives it could be related to an allergic reaction. Neither of those seem likely given the length of time his symptoms have persisted.
I know that may have you looked in his mouth but sometimes it takes a very close look under sedation to find the problem. If he will let you examine the inside his mouth again closely for swelling, reddened areas or any sign or trauma or a foreign body.
Ideally he needs to be seen by his veterinarian on an emergency basis. I am concerned that he got into something that was organ toxic and he is in organ failure given his symptoms.
In the meantime you can give him acid reducers to try and settle his stomach in case this is related to nausea. 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 will reduce stomach acid and may help settle his stomach. These are quite safe and can be used for several days if necessary.
A couple hours after one of the acid reducers is given offer a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 plain, boiled, white rice. Give small meals several times a day. Feed the bland diet for several days and he is feeling better and eating well, then start mixing in his regular diet and slowly convert him back over a period of 5 to 7 days.
If his drooling continues in spite of using an acid reducer and a bland diet then he should see his veterinarian for an examination, some blood tests to look for underlying metabolic disease, possibly sedation to look closely in his mouth and take dental radiographs.
Please let me know if you have any further questions.