What are you feeding Roxy , is it kibble, and are her teeth good enough to chew it. If not, I would switch to canned or soak the dry food in broth to soften it. Our dog is 15 and doesn't like the food hard anymore. Ours also has a lot of stiffness, especially on stairs. We make sure we only let her out on the stairs that are easier for her, not the steep ones. Is yours on pain meds the arthritis? Ours also sleeps a lot, also, and loves to do it outside, even in wet grass. I don't think Roxy is still depressed about missing her companion, but it is possible that she goes outside to distance herself from a frisky puppy and likes peace and quiet. Its so hard with an old dog, you know its just a matter of time, . We figure this will be our dogs last summer, hopefully she'll go on her own terms, but it seldom works that way.Good Luck.
Wow I am so sorry Roxy is barely able to walk any more.
The thing is there are a few other physical indicators that could be symptoms of something else. Change in appetite and physical activity can be neon signs when it comes to physical health of a dog.
It sounds like Roxy's activity level sounds like it has completely changed like night and day. That is a red flag even though she is aging. Especially since you foresee her possibly losing more weight in the future at the rate she is going.
I have seen first hand how sad it is when one dog grieves for another. In fact we are having to face putting one of our dogs to sleep and I know her brother is going to be as devastated as we are.
I am not saying your dog is totally depressed but of all the symptoms you are outlining I would see what a vet has to say. Have the vet gauge Roxy's quality of life right now and maybe determine if something else is going on.
Be prepared for the cost of lab tests if you do decide to take your dog to the vet especially if nothing leaps out when the vet does a physical exam. I am not saying this is what your vet will do but it is possible. Plus it depends on the extent you want answers.
I wish you the best with Roxy as well as your new puppy :)