So here's my ankle story. I am certain you will get all sorts of advice, but this is what I experienced.
20+ years ago, I both did a lot of backpacking and played volleyball. Every other weekend I was either working at REI, went backpacking, or played in a volleyball tournament. Then one unfortunate day, I severely sprained one of my ankles in a tournament. Once I recovered, I started using Active Ankle braces (http://www.allvolleyball.com/product/active-ankle-brace-t1/) which have proven to be very helpful for volleyball.
Now back then, I wore all-leather Asolo 555's, and never experienced ankle issues while wearing them. I had "almost" rolled my ankles quite a few times, but never to the point of causing a sprain. After my injury, however, I went on a few trips using the Active Ankle brace inserted into my boot, and while it was bulky, it was sturdy. Soon, I was back to "normal", so I quit using the braces, except for volleyball. And about five years ago, I started using a pair of trekking poles, and continue to swear by those to this day.
Two years ago, I started trying to use Inov8 trail shoes for backpacking, but it only took a couple miles into my second backpacking trip with them that I rolled my right ankle. It wasn't a severe sprain, so I decided to keep walking. But then mile or two later, my left knee ligaments started flaring up. By the end of the trip the following day, my ankle was fine but my knee was in severe pain and I could barely walk straight.
Finally just last fall, I was only about two miles into a Philmont prep trip with my Scouts, and the exact same thing happened: I lightly rolled my right ankle, I kept walking on it, then about a mile later, my left knee ligaments started aching.
So, I decided to re-sole my old Asolo 555's, and use those for the rest of my backpacking trips this past year, including our 85 mile trip at Philmont this summer. I have not had any ankle issues or knee issues since I switched back to the boots.
While I'd love to use my Inov8's for backpacking since they are considerably lighter, and I often run in them, they have not proven to work well for me while backpacking, even with trekking poles. I have heard many say that one needs to "condition" their ankles more with low top shoes, but in my experience; it much more complicated than simply doing that. Some people also say that they average mid-height hiking boot doesn't offer much toward ankle support, but again, in my experience, my boots offered me "just enough" support.
So given your history, I would definitely keep stability at the top of the list, and shoe weight second. Try to find a shoe/boot which can most comfortably work with your brace.
good luck,
Matt