I'm in north carolina so my main concern with weight is when they get wet or have snow on tthem. Would i have a problem if i planted the vines outside the run and the chickens peck the vine as it grows?
Snow shouldn't be a problem since you more than likely will have them pruned back before the snow flies. Water weight might be a problem, I just don't know what your set-up looks like or how strong it is. There shouldn't be a problem with the chickens pecking them outside; read what I posted earlier about height and protecting them.