Well, I was thinking that it would be more 'every god was technically involved, but some may have come in later or earlier than others'. So someone like, say, Hermes could possibly have more of a following than someone like, say, Zeus.

(I'll probably use 1d20 to determine their influence over the realm aka how long they've been around).

Each weapon I was thinking would have two forms, one in the weapon's natural state (like, as you stated earlier, Poseidon's trident) and one in a "sealed" form. In theory, his trident could be sitting at the bottom of the sea as a seashell for all we know.