We worriers will probably never stop worrying (more's the pity), but what we can learn is that MOST of these worries never come to pass. Over time, that's proven to us, and eventually we can acknowledge, then dismiss our worries based on the very real experience of their dire predictions never manifesting. It's like an itch, or the nagging feeling that you haven't locked the door when you very clearly remember doing it. Eventually, I think, we ignore them, distract our minds with something else, and they'll go away.
And wouldn't that, in the middle of a sleepless night, be a relief?