The title pretty much says it all.
My guess is because it would take a lot of effort to extract the Np-237 from spent fuel, and the weapons would only be “as good” as U-235 devices, which are much cheaper to make.
Basically nobody’s got round to it yet. 
Because U[sup]235[/sup] occurs naturally, we used that first; because it’s cheaper and faster to produce Pu[sup]239[/sup], we use that most. Np[sup]237[/sup] can be chemically extracted from spent nuclear fuel rods, but we’ve already got infrastructure in place for the other two.
Oh, and Pu[sup]239[/sup] has a smaller critical mass than U or Np, so there’s that.
Googling indicates that it’s not naturally occuring. Or, only trivially naturally occuring. This source says “researchers found minute amounts of neptunium in naturally occurring deposits of uranium ore. There is far more artificially produced neptunium than there is naturally occurring neptunium.”
So you’ll never mine neptunium, except as an indetectable byproduct of mining natural uranium.
Now, neptunium-237 is a fairly stable fissionable radioisotope, and it is an extractable product of breeder reactions, like plutonium. So, theoretically, it could be used in a fission weapon. (Not as a normal thermal-neutron chain reactor; apparently, Ne-237 captures fast neutrons well, but thermal neutrons not so well.)
However, the basic critical mass of Ne-237 is as high as that of U-235, and Ne-237 is probably as hard to extract from breeder waste as plutonium, but plutonium’s critical mass is 1/10 of neputunium or uranium, so if I had to pick which fissionable element to extract from nuclear waste, I’d pick plutonium, since I’d get more weapons out of the same mass of extracted fissiles.
ETA: Ninja’d because of my damn wall of words. However, I’d like to point out that Neptunium is used to create plutonium by neutron bombardment. Mars Rover Curiosity is warmed and powered by a plutonium RTG, fueled with plutonium transmuted from neptunium.
Next would be the Jupiteronium bomb.
There was also the discovery that Plutonium could not be used for a gun-type weapon. Because implosion was a *much *more complicated system and nobody was sure if it would be perfected in time (or even at all) they hedged their bets and pursued a gun-type using Plutonium as well (witness, along with Fat Man and Little Boy, Thin Man). They soon doscovered (I think just through mathematical prediction) that Plutonium fissioned too fast for it to be used in a gun-type design.
And after that, the only explosion left is the Solaranite.
This would also mean that Plutonium is no longer considered an element!
It does not have a fissile isotope.
Neptunium-237 is on that chart.
It doesn’t conform to the rule of thumb cited on that page:
I bolded “nuclear fuels” because I pointed out earlier that Neptunium’s fissionable isotope doesn’t make good nuclear fuel: it’s not particularly amenable to thermal neutron capture, so apparently only really good for fission explosions.
Neptunium-237: Atomic number 93, atomic mass 237, neutron number 144.
I would speculate with my undergraduate physics background that the “odd atomic mass/even atomic number” rule of thumb might be part of the reason for the “not good for nuclear fuel” thing.