Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you today. I do apologize that your question was not answered before. Different experts come online at various times; I just came online, read about your situation, and wanted to help.
Now I appreciate that you are worried about the cause for Benny's weight loss and his cough. And at his age, there are some serious concerns that we do have to consider. Still, it is always best to have these difficult issues looked into sooner rather then later. So, it is good that you are having him seen. As long as he is comfortable generally, you have nothing to fear about this being a "final" vet visit or anything like that. Instead, this is a chance to get to the root of his signs and take treatment steps to clear or at least reduce these for him.
Now since he has had weight loss alongside this cough, we'd want to make sure that further to a full examination (which include having his vet listens to his lungs and heart to help narrow down the trigger for that cough), that we consider having a geriatric blood sample tested. This will help make sure that our weight loss here isn't related to an organ issue (ie kidney, liver) or brewing metabolic disease (ie diabetes, etc). Furthermore, his vet's exam will help rule out heart disease (which can cause soft coughs) and again if this is localized to the lungs or throat, then they can help you determine if we have an infection, inflammation, or something more that we need to address. So, with their exam, it will give Benny the best chance here.
Finally, in the meantime, to just soothe this poor throat, you can try a mild cough suppressant. Pet safe options we often use are Glycerin/honey cough syrup(with no drugs in it) or even plain honey. Both can be very soothing and can be given at a dose of 1-2 milliliter (~1/4-1/2 teaspoon) as needed. Alternatively, we can use Robitussin DM. Of course, if you use this, we only want to use this one with Dextromethorphan +/- Guaifenesin. Avoid similar syrups with dog toxic drugs (ie Paracetamol, Acetaminophen, Pseudoephedrine, Phenylephrine or caffeine, etc). Dose-wise, you can give 1/2 (half) teaspoon per 10lbs of body weight every 8-12 hours. Again, these can reduce throat irritation and coughing for our wee ones.
Please take care & best wishes for Benny,