Before anything else, I do not aim to just make the PCs want to keep the weapon. I have rather specific criteria, and not following them will earn your question an avalanche of downvotes. Please read the question in its entirety before answering, as your schoolteachers told you to.
In a campaign I'm planning, one of the first quests is a simple gopher mission given by a farmer (we'll call him Chekhov). As a reward for this, they get Chekhov's Sword, which is more a rusty heirloom mantlepiece than Ultra Doomsmiting Stabby-Slicer Of Orc-Shredding. Still, it'll have use later, so I want to make sure the PCs don't hock it off at the Local Loot-Pawning Shop™ or chuck it into a lake or something.
There are four main obstacles:
- The sword can't be too powerful or valuable, or either the impoverished farmer would've sold it himself ages ago (not to mention the PCs would want to liquidate it themselves that much more quickly) or some PC would use it for themselves.
- I don't want to be too blunt or obvious, because I do not want to railroad the PCs into keeping it and I want to see at least a modicum of deductive reasoning be used later. (This is also why I don't want the PCs using it under normal circumstances.)
- The PCs aren't particularly sentimental, aesthetic, or trustworthy (so they wouldn't keep it for memories, decor, or to honor a request — dangerously pragmatic for writing a Chekhov's MacGuffin in). In fact, they're pretty much psychopathic murderhobos.
- The sword's main value is its sentimentality to the farmer. IT HAS ABSOLUTELY ZERO INHERENT VALUE OTHERWISE. The party cannot know why this is so valuable, though.
The idea is that it'll be useful later for a "I Know You're In There" battle with the farmer. Right now, though, there would be no reason for the party to ever think said battle would happen.
So, how can I make sure they hang on to the sword despite all that?
Best Answer
Let them sell it. Later, when they realize they needed it, let them troop back and buy it again. It can be a little mini quest: "figure out what happened to that sword we vendored".
I think your more general problem is that "the sword you need was coincidentally given to you as a reward for a fetch quest when you were low level" is already pretty hokey. So, if you really want something realistic, you might need to rethink your basic premise.