I'm not sure how well the "normal" hot wire is going to work against weasels. They are relatively small so could likely get past most of the usual setups.
Assuming you have an apron or foundation down that would prevent them from digging under (they live in burrows so they can dig pretty well), one option might be to put up a couple feet of 1/2" hardware cloth around the base, then at the top of that, run a single hot wire spaced no more than 1" out from the insulator supports. Goal would be have them hit the hot wire while climbing.......and yes they can climb too. If you were going to do it that way, tie your fencer's ground wire to the hardware cloth so hopefully they would be hanging on it when their nose hits the hot wire. You could tie to the ground too, but you may not need it if the cage wire is grounded. I wouldn't think you would need a super hot fencer just for this. Most any of the smaller units would work. If you got a small unit with solar charger, and face it to the south so it charges, it might sit there and perk along for a year or two with not much maintenance. (BTW, this assumes you have no overhanging trees or such to allow them an alternative path in other than climbing the run's wire walls).
To get around the door, cover the run door with 1/2" hardware cloth, or my preference, which is 1/2" x 1" welded wire, then run the hot wire up and around the door frame, then back down to the top of the hardware cloth on the other side.
I've come to believe that as long as you keep them out of your coop, weasels may not be as bad as we think. Their #1 prey is rodents in the form of rats and mice. They say, given a choice, they will prey on them almost exclusively. If so, one way to keep them away from your setup in the first place is to eliminate any spilt feed, etc. that will draw rats and mice to your coop. I'm wondering if many of the weasel issues are not weasels initially drawn to the coop by the rats and mice and being opportunistic little killers, they find the chickens and go for them too.
If you ever do discover you have a weasel hanging around, even more so if he ever gets lucky and kills something, probably best to have a weasel box trap built and at the ready. Just a simple box trap, with a small hole in one end and a big ol Victor rat snap trap waiting inside. Bait it with bloody chicken liver.
