Let me begin by admitting that my title question is misleading: weevils are different from most beetles in a very recognisable way but they are in fact still beetles, a family within the order Coleoptera which includes longicorns, elephant beetles and all the others.
Wikipedia informs us that Curculionidae, “the “true” weevils (or “snout beetles”) … are one of the largest animal families, with 6,800 genera and 83,000 species described worldwide.” It’s not surprising, then, that, “with so many species, a spirited debate exists about the relationships between subfamilies and genera,” (Wikipedia’s polite way of saying that the experts are still arguing).
CSIRO’s invaluable site says that weevils are, “Highly variable in form, but usually moderately to strongly convex, robust, heavily sclerotised and often clothed with scales or bristles. Head always more or less produced [i.e. extended] in front of eyes to form a rostrum, which is usually much longer than broad; antennae always geniculate [elbowed] with long scape and more or less compact club.” Many of those features can be seen in my photos of an individual I found in my garden recently:
What my photos don’t show, unless you’re very familiar with the texture of frangipani bark, is how big the insect is – just over 20 mm from snout-tip to tail. Most weevils are much, much smaller – under 6 mm – like the two at the bottom of this page.
Many species are economically significant pests of crops, laying their eggs inside seeds which the larvae consume before emerging to mate and repeat the life cycle. Many restrict themselves to one or a few host plants (just like, for instance, fig wasps and many butterflies) so that knowing the host plant tells one the weevil’s species. That doesn’t help in my case, however, since I spotted mine on a window and only moved it to the frangipani for a nicer background. Fortunately, a kind member of the Australian Insects group on flickr has identified it for me: Leptopius sp.