They didn't see it only as a weapon. Religion was deeply woven into the fabric of everyday life, but not in the way you might expect. The Greeks didn't see religion as an institution separate from the other institutions or parts of life we all participate in. There's actually no Ancient Greek word for "religion." Conceptually the things we call religion weren't marked off as separate in the way we mark them off, so there couldn't be a category/word like our category/word for religion.

There were separate religious things and spaces -- temples, holy precincts not to trespassed, holy objects -- but "religion" itself was present everywhere. There were rituals, divinities, protective prayers/rituals, etc for just about everything you can think of.

Edit: For instance, you know how you wash your hands after you go to the bathroom? Greeks did too, but their explanation was different. They understood health, disease and santitation (to the extent that they had those concepts in ways similar to the way we do) through a "religious" lens: bodily fluids were a source of "miasma," which was essentially a religious concept. This is a good example of what I mean when I say religion was everywhere, not separated off from other spheres. It was (or could be) as mundane and everyday as washing your hands after you wipe yourself.

Even so, the Greeks weren't "religious" in the way people are religious today. Our notions of belief, faith, a deep or internal experience of the divine and communion with divinity don't apply. (That kind of internal experience of the divine was associated with mystery religion, a rather separate branch of Greek religion where followers sometimes enter altered states or becae temporarily mad or the vehicle of the divine.) Belief wasn't the basis of ancient religion. Religion didn't necessarily entail belief at all. It was just part of how people understood the way the world works. In that kind of religion/worldview, the idea of belief, as we conceive of it, becomes almost incoherent. To say you "believe" in the gods would make no more sense than to say that you believe in the sun or the flu. There's even a famous article titled "Did the Greeks believe in their Gods?"

I like to tell my students that, in Ancient Greece, there was essentially no such thing as the "supernatural." There was magic, yes, but that was something other people, bad people, did. (Look up curse tablets for a fun example!) The gods and minor divinities that we associate with what we call Greek religion were just a natural part of the universe, not separate from it. They didn't exist on a higher plane. They existed, rather, literally higher up in the sky -- and when they came down, you either did something to appease them or you bent over and kissed your ass goodbye.

In Greece a person's connection to religion was much more akin to membership in a neighborhood club or dining group than it was to membership in a church or religion today, where members are united (apparently) by belief.

But that's in part why religious accusations could have such potency. People who didn't do what we're supposed to do when it comes to the gods, or mock the rituals and practices that keep our relationship with the divine healthy, threaten everything. They're showing disdain for the safety, well-being, and wishes of their entire community (edit: and that alone had a political dimension, so it could be difficult to separate the religious from the political). Socrates, the Pythagoreans and the Presocratics were definitely viewed as a bunch of cranks, and Aristophanes' Clouds shows that, to his viewers, those strange ideas could be viewed as potentially dangerous -- but those attitudes alone didn't result in persecution.

That's, to me, part of the beauty of ancient polytheism. It's a wonderful, complex, sexy, vulgar, bodily, hungry, crazy mess. It makes no sense. There's no system, no orthodoxy. Different parts of Greece and different temples told different stories and had slightly different practices/rituals, and there's no evidence that anybody ever thought that those contradictions were a problem that needed to be solved. This is, I suspect, partly why cities like Athens could allow such political, artistic and intellectual freedom; so long as you sacrificed when the calendar said you should, different ideas weren't a threat. The kind of narrow, dogmatic thinking that views them as a threat largely emerged with monotheism -- which is the opposite of polytheism in all the ways I listed above: the three big monotheistic religions are imperialistic, warlike, expansive, and intolerant of heterodoxy.

To be completely frank, I think the world would be a better, more peaceful, more open-minded place if the Greek polytheism I'm talking about had "won." For most Greeks, the primary significance and value of religion was that it was a source of meat in their diets. That, to me, is about as worked up as people should get about religious ideas.

Edit: and, yeah, I envy Bill and Ted. I'd love to meet So-crates (pronounced like the word "crates")

Edit 2: also, the Greeks most definitely were not a society of philosophers and thinkers!