I understand that a question similar to this one was asked earlier. But the same thing happened to me, because I bought my dog a new stuffed toy, and now he carries it around in his mouth wimpering. I don't know why, he seems to enjoy the toy, he chews on it all day, and what not. He also gets plenty of exercise and attention, so I am not sure what could be causing this. Any ideas?

Try giving him extra attention. My puppy does the same thing so we go out and throw the toy for him.

Here is a link to a post that is like yours. You are not alone in this issue.
https://www.askmehelpdesk.com/dogs/crying-happy-dog-115348.html?highlight=westie

If he plays with it all day long and hasn't torn it to bits, I wouldn't worry about it. He is deriving some sort of pleasure from this. If he didn't, he would ignore the toy.

Sometimes my dog (now 1 yr 4 months) will walk about whimpering with one of his favorite little cloth stuffed squeeky toys. It doesn't happen often... but it's sort of cute when he does it. I think he may be feeling that he'd like to bury this impoortant object... as if it were a bone. A few days ago I gave him a large dog biscut. The big dog size... but he is a small dog (nine pounds). He carried the biscut around the houuse from place to place and was obviously trying to find a good place to "save" it. He's set it on the couch and then tried to dig around it. Tried to push couch over the bone to bury it. So cute.
I asked him "do you want to take your bone outside?"... and he went to the door. I watched him out there with it... as he buried it in my flower bed.
It's still out there and he checks on it every couple dayys. Sometimes he movves it to a new area.
So... I think your pup is just in love with that toy and sometimes he's concerned about the best place to keep it safe. It's an instinct I believe.
Give him other toys to choose from... but that will probably be his main favorite.