Officious may have been derived from two different Latin words whose meaning were combined together.  The first Latin word was officiousus, 'sounding something like a spell Hemione Granger took great pleasure in pronouncing', and meaning kindly and obliging.  The other word is officium, meaning service or office, so it seems these people think it's their duty to give others their advice, which is sometimes cloaked in a sweet, sappy manner.