One at a time. Systematically remove the threats; don't spread your resources too thin.
Voting for yourself is not necessarily a "goon" trick. It is a survival trick, either to make people think you have nothing to lose and are therefore vanilla, or you have everything to gain and are therefore jester. As a cop, voting for herself - indeed, getting herself lynched - would serve only to incriminate Jason Statham, and even then, only potentially. The potential for an honest Weaver to be insane is there, and that would mean two (potential) deaths and losses of power roles for naught.
Weaver's strategy is strange, her actions and words contradictory, and her targets unfounded. For those reasons, I think we should lynch her.