Click diagram to biggify so you can read it more easily....
I've mentioned a couple of times that the yarn I'm working with is really a knitting yarn - it's very softly twisted and therefore wasn't standing up very well as warp, tending to shred in the reed at the selvedges.
The way I deal with this sort of issue is to thread the selvedges to compensate for this inherent weakness. Since I'm weaving plain weave, I double the ends in the outside two heddles, but keep the density the same in the reed. When I'm weaving a twill, I thread the outside four ends doubled in the heddles and again, keep the density the same in the reed.
If you double the density in the reed as well as the heddle, the fabric is twice as dense there and will tend to not beat in at the same rate as the rest of the cloth creating a 'smiley' fell line. It will also look different than the rest of the cloth.
I also do this for very fine threads that are a bit on the weaker side. It really doesn't show and makes life soooo much easier when you don't have to deal with shredded selvedge threads!