Neighborhood watches involve night time patrols, and evenings are when criminals come out to play. In addition, neighborhood watch people are looking for trouble, though in the sense of finding and reporting criminals rather than arresting them. If they run into criminals on the job, and the perps are armed or numerous, their lives could be in jeopardy. It would not make sense to have a neighborhood watch without weapons. I've read about neighborhood watches in Third World countries where gun control is pretty strict. They carry fighting sticks or batons in case of attack. The irony is that any neighborhood watch where weapons aren't needed is probably a superfluous neighborhood watch.
People who are against neighborhood watch people carrying guns are a little naive. Criminals who might hesitate to attack cops have no compunction about attacking civilians. Mayberry* was 50 years ago.
* If San Diego PD's stats are to be believed, per capita violent crime was much lower 50 years ago; better emergency medical care has turned many shooting and stabbing incidents that would have become murder cases back in the 1950's into aggravated assault cases today. In 2006, per capita robberies were 6x what they were in 1950. Per capita aggravated assaults (shootings, stabbings) were 15x.
Houston has strict no-weapons policy for its neighborhood citizen patrols. (It has actually three programs, but the patrol program is the relevant one.)
This policy had unfortunate consequences for a Citizens on Patrol (then called C.O.P.) in a black neighborhood in north Houston called Lexington Green, 20 years ago. The patroller saw a suspicious car, suspected that the house nearby had been entered, and started writing down the license plate. He never finished -- the armed "burglar" inside came out and blew him away. Another black-on-black crime statistic, for a guy who followed the rules.
Houston then instituted a new rule, which was that a patroller was never to leave his vehicle. Which conflicted with state "good Samaritan" laws and laws against "failure to render assistance". But the policy remains in force today. Even for cyclists who join the program. Some people patrol on foot (the gay community in Houston were doing that, looking for gay-bashing cruisers like the ones who murdered Paul Broussard near a Montrose gay bar in a case notorious from 20 years ago), which creates another cognitive dissonance within the program.
In Dallas, a very bad area that had numerous armed dealers and dopers staggering around started their own group within the Citizens on Patrol umbrella program 15 years ago. They were all older black men in their 40's and 50's who patrolled in groups of five or six on foot, every one of them carrying a shotgun. They weren't playing. They didn't lose anyone that I ever heard of.
I tend to think that when you’re talking high crime areas, police patrols should be stepped up and not left to (generally) untrained civilians, i.e., anyone who signs up and is willing to give a night of his/her time here and there. But in reality, police cannot be everywhere, and they cannot even respond quickly enough for some urgent situations.
A vehicle beyond Neighborhood Watch is needed for high-crime areas, perhaps something along the lines of the Guardian Angels. In those areas where you need armed patrols, they’d have to be identifiable, well-trained, kevlon-vested, and deputized backup to the police.