Howdy Folks!
From what the OP has told me, there is more than the possibility of encountering nefarious types there. Evidently, it is a risky place for decent folks to tread without means of self defense. So prohibiting weapons would only affect law abiding citizens. Miscreants will blissfully ignore that prohibition as they bring weapons to the location in order to perform their various miscreancies. Why is it that the law abiding citizen is reduced to exposing him/herself to victimization? By law, no less.
Just an interesting side note; if there is a sign prohibiting "weapons" per se, I'd need to strip naked to visit that park. After all, I can make use of darn near anything as a weapon. For example, snap a credit card in half, and both rough edges can cut just as good as any knife you might wield. Granted, they don't snap in half easily, but once you develop a technique, it can be done in reasonable time. Then again, I usually wear a belt, and that too can be used as a weapon. Or how about shoe strings? Or how about some of the various digging tools I often have on my person when metal detecting? Or how about dirt that often remains in my pockets after metal detecting? Or if I've just been metal detecting, there is likely to be all manner of sharp objects in my pockets. For that matter, a handful of well thrown coins can do some damage at close range.
Then there is always the guy who has a degree of martial arts training, and therefore, his hands and feet are considered weapons?
See where I'm going here? In order to prohibit "Weapons", they'd need to define their definition of 'weapon'.
Heck, somebody walking a dog with a chain leash can inflict a whole bunch of damage with that chain.
The point is, the word 'weapon' is, in and of itself, somewhat ambiguous.
Blessings,
M-Taliesin