Loose Selvedge Threads
I am a relatively new (1 ½ year) weaver having a blast. I’m working on a set of Lee’s Surrender table runners now and it is going well. But the selvedge threads (maybe even the last two) on each side are becoming lax and require a couple of S hooks such as I usually use with floating selvedges. I’m sure there is an explanation for this—maybe as simple as poor loom dressing. Please enlighten me. Also, is there a way to wet-finish the runner (10/2 pearl cotton warp and tabby weft, lightweight wool pattern weft), so that the wool doesn’t full too much?
Welcome to weaving! First of all, with Lee's Surrender, which is an overshot draft, you should be using floating selvedges (I'm thinking you are). Their purpose is to bring every weft around the last thread on each edge of the cloth, which the weft might not do if the shafts for those threads are down for two picks in a row. To make the pattern and tabby wefts quick to insert without worry about interlocking them at the edges, a floating selvedge is a plus when you are weaving overshot (the pattern weft might not otherwise interlace at the edge). I'm assuming that since your floating selvedges are weighted with S-hooks, they are not becoming looser.
The threads next to them on both edges may be getting looser because of the interaction of two factors. First, it is important that all warp threads be wound TIGHTLY as well as evenly on the warp beam. If they are not wound tightly, anything that happens to pull on a single warp thread or group, will pull against those threads so that they tighten more than the others on the beam and therefore become looser than the others at the fell. If there is draw-in during weaving, the edge threads crowd a little more closely together. The weft can't pack in as tightly where warp threads are closer together (it's as though you've changed their sett), and the fell of the cloth becomes a bit closer to the reed in their area. That means that the reed hits those threads harder and sooner than the others, pulling against them. If they are wound on the beam a bit loosely, they tighten there and become looser at the fell.
It sounds like you don't have very much draw-in if only one or two threads are behaving this way. I'd just wind the next warp on the beam so it is very tight.
As to your other question: I must confess that I don't wash the overshot I've woven with a wool weft (these are mostly coverlets) simply because I don't want the way the cloth looks to change with any fulling of the wool. I recommend dry cleaning only (and also confess that I plan for them not to get dirty). To wash them, as normal people would want to do, just do everything you can to avoid fulling (wash and rinse in cold water, by hand, with as little agitation as possible).