Need Help Melding chicken Wire

Well not sure how to do what you want, but chicken wire is to keep them in it will not keep predators out. You should be using hardware cloth for that.

I would install the cross piece and staple to it

I thread wire through the mesh on the overlap.

Most farm supply stores around me sell "cage clips" and the tool to put them on.
It will join the chicken wire together but as others have stated stronger wire is better at keeping critters out.

I also have 7ft tall run.  I have installed cross-pieces in my run area just for that purpose.  To much flex in fencing otherwise.  I will post pic when I get home.(can't figure it out with my tablet)

I also have 7ft tall run.  I have installed cross-pieces in my run area just for that purpose.  To much flex in fencing otherwise.  I will post pic when I get home.(can't figure it out with my tablet) oops, I do have pics on my BYC page.

Rewire ties would work and are really fast if you have the spinner.

We built our coop this summer, and it is elevated about 18" off the ground, so we put 36" hardware cloth halfway in the ground and attached the other end to our coop. However in our run we bought some tin from an old barn (cause hardware cloth is expensive) and did the same thing in our run, burying it and then drilled holes in it and wired our chicken wire to it. That prevents any varmints from digging under, and allows the chickens a place to get our chickens out of the sun on the hot summer days (under the coop) while also providing a good breeze way. I did some research and found that if you bury 1/2 or smaller hardware cloth at least 18" in the ground it prevents even mice and rats from being able to get in. They would just go through chicken wire, also a dog would be able to tear through the light chicken wire. i figure the tin works better than both and was almost free.
So that is what I would recommend. we cut a piece in half and buried it flush with the ground where our gate is it works very good also. I hope this helps and that it makes sense. Merry christmas and Have a blessed new Year

Our yard is 7 foot high at the roof peak and I used   two layers of chicken wire top to bottom then added a layer of 1/2 inch welded wire from 18" under ground to 4 feet up. I re purposed the wire used to bind the rolls of welded wire to knit together every place wire overlapped. There are 2 x 4's at about 2 .5 feet off the ground and I used heavy duty metal hammered in staples (over two pounds used ) to secure the wire to the wood. Our "soil" is sand and I have raked a 3 foot area around the entire perimeter of the coop and yard and walk around the perimeter every morning to see if anything has tried to dig in or come through the wire.
Yes, knitting together the different wires took quite a bit of time and while I was knitting friends and family joked about my efforts but man is the yard beautifully secure and safe for the hens.