DISCLAIMER: This is just my superficial analysis, not based on scholarly research (alas), nor based on any sources.
Along the lines of Andrew J. Brehm's answer, I think there is something to the notion that this form (or class, if you prefer) indicates that the noun is "fit for" the associated verb when such a verb is applicable (bari does not have such an easy to pinpoint verb; is a "healthy" person "fit for" creation, or "fit for" being made healthy?). I think, though, that it is more that the the noun is passively described, almost as an intransitive noun connoting the state, or, rather, the definition of that noun.
I don't believe this is inconsistent with Ibn 'Ezra or Gesenius, but, perhaps, more defined.