Easier said than done.
I'm not sure if I want to include this post as part of the Slender Man Doctrine, but it kind of fits. I wanted to take a moment to look over the various defenses the thing possesses. Not a specific abilities rundown, but rather just a "This is all the shit you're going to have to go through if you want to hit it." Which is somewhat important because... I don't think it's so much a matter of finding the right weapon to fight the Construct with, so much as it is finding a way to actually CONNECT with said weapon. So here we go...
Firstly, to strike the Construct, you need to consider the base levels of protection that it possesses. I'm going to address these as "Layers," of which there are three.
Layer 1 - The Malleable Body
The Construct is capable of changing it's shape. Twisting, stretching, and contorting itself beyond our feeble imaginations. Becoming taller, elongating his arms and/or legs, growing new limbs from seemingly nowhere. This is a pretty clear indicator of a physical make-up that is more like clay or... jello, than a truly solid substance. As such, I believe it is presumable that the Construct's body could easily absorb and/or deflect any direct attacks, bouncing back from them as though he hadn't even been touched. (Go poke a big slab of jello really hard, you'll see what I mean.) It's even plausible that the Construct could perform a form of rapid self-healing in the event that such a near-liquid body was punctured or cut.
Layer 2 - Tentacle Onslaught
Whenever actually threatened by something, or perhaps just when motivated/annoyed enough to do so, or just for kicks... I don't fucking know... the Construct brings out ye old flailing appendages. These things serve multiple purposes and act as much as an offensive structure as a defensive one. Though I could note that "the Best Defense is a Good Offense" so whatever. These things act primarily as a distraction, they draw the eyes with their constant, rapid movements. This makes it more difficult to maintain your aim when the target's body is constantly obscured and/or moving about. Additionally, they serve the obvious purpose of keeping you from getting anywhere near close enough to attack the first Layer directly. The number seems to vary, though I imagine that the more of a threat you are, the more you're going to see... until there are so many that they're the only thing you can see.
Layer 3 - Perception Barriers
Note the "s," plural. The Constructs greatest weapon is, and has always been, it's ability to affect the mind... through what I assume is some means of psychic activity. There are any number of mannerisms that I've observed through my studies that you might come across. Perhaps one of the more frightening is the ability to make himself invisible to the human eye. This approach is selective, seeming to only work on certain individuals... but regardless, it allows the Construct to hide from you while in plain sight. As in, standing dead center in front of you in a wide open empty space and you still don't see anything.
Another instance is an apparent ability to stop an individual dead in their tracks. Causing the body to simply lock up and be either extremely difficult or damn near impossible to move. There may even have instances in which the Construct has taken control of the victim through use of this version, forcing them to move how he wants them to or perhaps just flinging them bodily across a room without actually touching them.
Yet another is the simple act of creating an actual physical barrier, which would react to those who encounter it and objects that strike it as an invisible wall. They stand as if to say, "You may go This Far, No Further." Effectively rendering any attempt to get near the Construct an effort in futility.
And perhaps the recent favorite is the Loop. Trapping your consciousness in a state of perpetual existence, apparently separated from the real world around you. These vary from the simplistic, in which you find yourself performing the same act repetitively in succession, the same moment occurring over and over again until the chain is broken... to the highly advanced, in which a large area has been isolated from the rest of the world and looped inwards upon itself, creating a perpetual space of nothingness, in which nothing ever changes and time is effectively non-existent. Such loops tend to only occur in extreme or special cases however, likely do to a higher level of effort required in creating and maintaining them. So they aren't the type of thing to expect often, but nonetheless are part of the Constructs arsenal of mindgames which prevent you from actively approaching him.
Lastly, a perceptive element that can be applied on it's own or in conjunction with any of the previously mentioned versions, is the Illusion. Just as the Construct can make himself invisible to your eyes, he seems to be able to make other things just as transparent... and things that aren't there at all, suddenly very real. Another of his most powerful tricks, the Construct's ability to make you see, feel, or otherwise "experience" things that cannot possibly be happening to you. By manipulating your perception, it can make you believe anything it wants you to believe... or at least, it can try to.
Each of these Layers is like a particular stage of a complex boss battle, in which you must find the weakness of each form before you can truly pierce at the heart of the beast. It would likely require a very well coordinated group effort or else one extremely gifted individual, to bypass each layer simultaneously and actually strike a damaging blow against the Construct.
However, it may also be possible to avoid certain layers entirely. The second Layer being the easiest to avoid, but doing so would require catching the Construct off guard. Which may be easier than it sounds. The Construct seems to rely on the third Layer most heavily, typically capable of rendering any foe helpless merely by directing it's gaze in their direction... but if one were capable of overcoming a given Perception Barrier, then one would have the opportunity to lash out at the Construct while it remained unguarded by the second Layer. This strategy is not foolproof, as I shall point out later in a "Case Study" I'm preparing, but it holds potential.
There is also the rare instance in which both the Second and Third Layer are cast aside. Typically in situations where the Construct WANTS you to go running into his open arms. Or maybe he wants someone else to and you just happened to be around at the right moment? Either way, it's a perfect opportunity to strike if you could time it right.
One last thing to consider however. I wouldn't necessarily refer to this as a Layer, but it is an important factor to consider nonetheless when attempting to attack the Construct and bypass the Layers that comprise his defenses. And that thing is SPEED...
For something that stands around not doing a damned thing so often, the Construct is remarkably fast. This should be obvious enough while observing the movement of it's slender appendages, but is not an immediately recognized fact in regards to the speed at which the Construct actually "Moves." This is probably misconception resulting from it's nature as a still fixture, standing in place, silently observing. I hesitate to suggest the Construct is capable of actual teleportation, supposing rather that's it's use of "the Path" accounts for its capacity to cross vast distances in short timespans. However, in regards to close range travel, the Construct is able to reposition himself at rapid speeds, almost the blink of an eye. Though reports of him "walking" are few and far between, there are documented cases which it, and the speed by which he flows across the ground has been noted as alarming. Henceforth, unless the Construct has chosen to fight you standing still, then piercing through each of those Layers is going to become increasingly more difficult.
These observations are not meant to discourage you from opposing the Construct, but rather to inform you of what you're going to be up against so that you may take proper precautions and (hopefully) not do anything stupid. Good Luck... and remember, that "Perception is Key."