different weapon enchants are based on items/magic/covenant gifts. Remember only non-elemental weapons can be enchanted, only some boss weapons, and only some unique drops. you can test which ones can be enchanted because it wont even let you try to enchant if you cant.
for example, you have these things called resin that can give weapons fire/lightning/poison enchants. you can buy these/drop from enemies. these have no requirements. Then you have enchants from magic that you buy/find/learn such as crystal weapon magic etc. these have int/faith requirements. then you have weapon enchants that are covenant specific like sunlight blade or dark moon blade. these require usually at least lvl 2 in a given covenant. these have covenant lvl/int/faith requirements but are usually the strongest.
you can join a covenant more than once, but there's a few things to take note of. If you join a covenant and then join another one, you will have committed a sin and broken the original covenant's rules. you cannot join that covenant again unless you ask for forgiveness. keep in mind leaving a covenant will mean all your levels gained in that covenant are reset to 0. leaving a covenant without committing a sin means going to the church bell tower and leaving the covenant first through him.