I patterned my 4 wire system after what Robert describes in that link. I find it works well, and with the wire system, you are able to enclose a much larger area for less expense and easier maintenance than using the poultry netting. Again, he suggests only 1 and 2 wire systems and claim they work well for him, and even more so with really large enclosures measured in acres. With my smaller area, I found the addition of the extra 2 wires (4 in all) to work best for me. BTW, the spacing from the ground is simply the 4 lowest clip points on those white step in posts. Those make the install a straight forward, easy process.
Poultry netting is a much tighter defense, but the strands are closer to the ground than with the wire, so grounding of the fencer is a concern. The fencer still shocks, at least while the battery is hot, but weeds will drain the power source faster. That may not be as much of an issue if you use an AC powered charger. Parmak makes one of those that is pretty potent as well.
Again, with weasels, they could slip through a fence like that with ease if it were only the fence. But a hot fence? My guess is they would get zapped and that might well deter them.
But if you know you have one, trapping ain't a bad option either. Better safe than sorry.
Lastly, I'm convinced that a lot of predator problems with weasels, skunks, snakes and such are our own fault. Most references say that the vast majority of a weasel's diet consists of rodents in the form of rats and mice and other burrowing rodents like gophers and moles. So we let the birds waste a lot of feed, the rats and mice move in to clean up the waste feed, multiply like rats and mice and the weasels then sense they are there and move in to take out the rats and mice. But being opportunistic killers as they are, quickly transition to our birds and just might kill them ALL in one frenzied attack. Not to eat em, just to kill em. Once they go into attack mode, they attach movement. They are good at it and go for the necks at the back of the head......kill that bird and move on to the next until there is nothing left to kill. Then they go home. Same with snakes. They come for the mice and rats, and find eggs and help themselves to those too.