The differences between meister and weapon is unclear. People argue about it
A weapon seems to be an ordinary human who inherited two specific non-human traits: The abiilty to transform (probably derived from the witch transformation) and the trait that dictates the type of weapon (probably derived from the witch code that dictates symbol animal is my guess). Some weapons also have elemental skill sets such as manifesting fire.
People born weapons appear to be able to decide if they want to use that skill or not, otherwise they appear to be able to live normal lives.
It's not yet explained in the manga if a meister is born or trained.
There is no common skill or trait set that is seen in all meisters, so it is possible they're ordinary humans who have no special or unusual traits. It probably would help to inherit certain skills (such as something in the soul perception/manipulation area) but nothing in particular seems required as far as we've seen. Everyone's got a little bit of something different.
For all we know, in the SE world, many or most people are born with the potential to develop stuff like soul perception but unless they have a need or reason to, the potential isn't reached. But we really don't know any of this from the manga.
And it's not clear how any of this affects resonance but I'd guess two people need to have compatible souls to achieve the deeper resonance to allow one to be wielded but something like team resonance can be achieved between any people who work at it. Probably two meisters could seriously resonate but if one isn't a weapon able to amplify and evolve a form reflective of the wielder's soul, what good is it? And a weapon and a meister could team resonate easily, but it isn't enough to allow incompatible partnerships. At least, that's what I'm getting from what's been shown.
Hope that's somewhat helpful.
adding: some weapons can solo pretty well, some can't because they just don't learn or just can't learn. I'd bet that Soul and BS could team resonate if Soul was actually fighting himself but there's no reason to otherwise. Heh, I don't think they'd have had a better chance against Kid even if they had known how back in that duel!