There's a very appropriate quote in the Observer today, in Peter Culshaw's review of Andy Cronshaw's "Ochre" album, which is a multi-cultural look at some English tradfolk tunes. The relevant bit of the review is:

"The disc is mostly instrumental( so you don't have to put up with twee lyrics about forlorn maidens)..."

   This seems to be a resonable comment, the "folk" scene is certainly infested with tweeness. I would add myself that, as far as I can remember, I have never encountered tweeness in the context of a traditional folk performance. Tweeness always seems to me to be added by non-traditional performers doing traditional material(whether classical arrangements, revivalists with guitars and long hair, or children being forced to dance round maypoles). Or alternatively, tweeness is mostly frequently inserted by modern songwriters working within the folk scene and getting their work classified as "folk", either by themselves or by the media.
    As a further comment on whether tweeness is always associated with females, I would say that the best way to explain the word "twee", to anybody who is unfamiliar with it, would be to suggest they listen to "Puff the Magic Dragon" by Peter, Paul and Mary; and two thirds of them were male. This is also a good example of tweeness being unfairly associated with folk. By broadening your definition of folk to include drivel like that, you inevitably tar the world of folk music with a twee brush, when real folk is completely innocent in this respect.