I read this short fiction about 10 years ago in a collection in English. More a novelette than a short story, I would say.
It is definitive not in the world of Tolkien, not even in fandom. There are, however, several "races" in the sense of Tolkien. Big People (or Big Folks ?), that is, us. Hinted at, but never seen in the story. Very small people, less than three feet tall, and their collective name is not Hobbits, but I don't remember what it was. These represent most characters in the story. Also one character, taller than these non-Hobbits, but smaller than Big People. His people has a collective name which is not Dwarves. Again, I don't remember what it was. Besides there are trolls, who are not turned into stone if sunlight reaches them, one cannot trap them like Bilbo did in "The Hobbit". Still, they are very sluggish in the daytime and prefer to hide from the sun and sleep. Also a huge spider, and more horrible antagonists.
The story begins when the non-Dwarf sells to a (young) non-Hobbit a map to a hidden treasure he claims to be too old and not adventurous enough to return to. IIRC, he says that the first time he found it, he had no way to bring it all back and took just a few handfuls of gold coins, of which he still has some.
The non-Dwarf has a horrible accent. I could not understand what he said without reading it aloud and trying to make sense of what I was saying...
So a party of non-Hobbits follow the map, fight antagonists, find the treasure but only bring back a few handfuls, like the non-Dwarf did.
EDIT
Judith Jones suggested The Iron Tower. It is clearly not my story, but there is something interesting in her answer.
She mentioned several names of races. Well the names Rucks, Hloks and Ogrus definitely sound wrong. One of "my" two races might have a name like that, but I don't think so. It sounds wrong, but I really don't remember anything about one of the names.
But she also mention "warrow". Now this does not exist in English except in fantasy novels. But in my french ears, it sounds "as if it might be" an english word. It is definitely not the name of the other race, it does not ring any bell. But it reminded me that one the races (I think it was the taller one, the unique "not-Dwarf" character in the story, rather than the many "not-Hobbits" characters, even shorter, but I am not positive) had a name that, like "warrow", does not really exist in English but "sounds" as if it were an english word. But I don't remember what it was, except it was not warrow, nor "halfling".