LH’s post on cleave put me in mind of this observation from John Steinbeck’s introduction to his Acts of King Arthur and his Noble Knights, in which he describes his first encounter with Malory as a child:
I was delighted to find out paradoxes - that cleave means both to stick together and cut apart, and that host means both an enemy and a welcoming friend
That got me thinking too. Another such word is let, which used to mean both to allow and to prevent (as where Hamlet says “By heaven, I’ll make a corpse of him that lets me"). The second sense is obsolete as a verb, although the noun form is still just about clinging on in the phrase without let or hindrance. And then there’s oversight, meaning both the act of supervising something and of forgetting clean about it. I’m sure people here can think of plenty more.