When I weave stitches through, I do it by the seat of my pants... I don't think I've ever actually paid much attention to all the great instructions I've read on how to do it
The one key that seems to work for me is to weave the ends through, then tug the fabric in all directions. What happens is that when I tug, the amount of stretch the fabric may encounter is taken into account and the woven end will loosen up some. Then I snip.
This doesn't make sense to me reading back so let me describe it another way;
After weaving the end through, snip the end as close to the fabric as you can without cutting anything but the loose end. Then stretch the fabric in all directions. What you will probably see is that that snipped end will get un woven for at least the last stitch it was woven through, because the fabric has more give to it than the single strand of yarn. The end you so neatly snipped close to the fabric will probably now be poking out. Snip again, close as you can, and give a stretch. It will probably remain hidden this time.