Play the game if: you like your IF compact, your challenges fair, and a little bit of narrative color around your puzzles.
Don't play the game if: you want a genuinely tough game, strong emotional investment, or a setting that provokes a sense of wonder or discovery.
The Weapon is probably a good introductory game for those who are new to IF. The one-room geography won't tax your memory, the straightforward command system won't offend your linguistic sensibilities, and neither the game itself nor the puzzles are particularly brutal or unfair.
The story resembles an escape scenario. You play something of a Hannibal Lecter figure, a criminal genius who is being brought in to investigate an alien artifact of great power.
What I like about this is that most of the puzzles have two layers: your objective is to learn about and activate the artifact, but you must do so in a way that will not alert your captors. This adds significant pizzazz and an extra challenge to what would otherwise be fairly light puzzles (though they're not straightforward).
The puzzles generally take the form of just requiring you to be observant: you'll need to consider the possible uses of pretty much everything in the room in order to progress. I must admit to having a soft spot for escape scenarios (having been brought up on Doctor Who), so this kind of challenge - improvising ways to evade your captors - is one of my favorites.
If The Weapon has any weakness, it's that it deserved to be part of a larger narrative. The backstory, while not uninteresting, can never come to life because it's more or less superfluous, and so comes across as a tweaked version of the backstory to Ender's Game. While the characterization and setting are well-written, certain events lose emotional impact because it's been too soon since we were introduced to the context. It's a shame because, without being specific, this isn't really the kind of game that begs for a sequel, and it seems doubtful that we'll see much more of this world.
Nevertheless, it's an enjoyable distraction that probably won't take you more than a couple of hours to complete, and for a distraction, it's rather well-written. The puzzles are genuinely engaging as the player needs to make a genuine effort to understand the particulars of how the story's technologies work (Spoiler - click to show)(as with trying to mask the transmission or read information on the viewscreen without Cheryl noticing).
Overall, if you have an evening when you have nothing to do and just want to relax, The Weapon would easily give you something fun to do - the equivalent of watching a light movie or re-reading an old book.