Tolkien never described Sting, or any weapon, to any great extent.
Sting, along with Glamdring (Foe Hammer) and Orcrist (Goblin Cleaver) were taken from a troll hoard in The Hobbit. Gandalf, the wizard, caried Glamdring throughout the Hobbit and The Lord Of The Rings trilogy. Thoren Oakenshield took Orcrist to his death. It was buried with him. Glamdring and Orcrist were both swords. Sting, taken by Bilbo Baggins and later given to Frodo, was a dagger.
All three were of ancient elvish manufacture. They had magical properties and actually glowed blue in the presence of goblin-kind.
Sting was directly described as a "dagger." For a Hobbit, it was almost big enough for a short sword. Bilbo stated thet it would only make a "pocket knife" for a troll.
What did these weapons look like?
These are the movie sword from The Lord Of The Rings
In movies and illustrations, the swords are usually represented as double edged, two-handed broadswords, almost Bastards. Glamdring is almost always depicted as double-handed. Orcrist usually is. Sting is usually pictured as a long, double-edged dagger, with distinct cross guard and pommel. These weapons resemble those from the High Middle Ages, or even Reniassance.
These depictions are a result of popular perception. Ask the average person to describe a sword, or a dagger. That's what you usually get, I have no doubt.
Sting is short enough to hide. Bilbo habitually carries it thrust inside his breeches. Anyone who has carried a knife in such a fashion knows that the blade can't extend past the knee. Hobbits are about 2-4 feet high, Bilbo is average height. Let's say he's 3'6". Figuring for normal anatomy, let's limit the blade length of Sting to 10 inches, probably less.
Some have claimed that Sting is described as leaf-shaped. I couldn't find that anywhere. The swords that Merry and Pippin took from the Barrow in The Fellowship were described as leaf-shaped. I don't think Sting was. Correct me if I'm wrong.
What do I think?
IMHO, Tolkien patterned his world not from the high midle ages, but from the world of the Anglo-Saxon/Norse. His imagery had more to do with Beowulf than Robin Hood.
Thus, his weapons would be Saxon weapons.
As far as Sting goes, the Saxons didn't distinguish between the words dagger and knife. I have no doubt they had double-edged knives, but not usually. I think in Tolkein's context "Dagger" meant fighting knife. He was a veteran of WWI they used plenty of daggers there, only they were called bayonets. They wern't double edged. Neither were the German "trench knives."
The Saxons had a special knife, beloved of my heart, the Seax. They were even named after them.
Seaxs were of all different sizes. They were more than knives, they carried cultural, and probably religous, significance. Only free men were allowed to carry Seaxs and they all did. There's evidence that even the poorest farmers carried these as tools and weapons.
Seaxs are thick, sturdy, single edged knives. They were usually carried edge-up in a horizontal sheath. As in our American West, knife-fighters were probably trained to hold their blades with the edge-side up. This lets you parry with the dull side more easily. Russian troops are still trained this way.
Here's what I think Sting looked like, far left:
( Here's a small norse Seax, reproduction from Urweg):
Here are the patterns for Glamdring and Orcrist:
What do you guys think??