Of the various joining methods for introducing new yarn, the one I guess that is most usual is to just overlap the ends a bit on the next pick of weft.
I read a lovely old manual for a Schacht loom that talked about how best to do this and how important it was if you were entering your work in competitions! Apparently judges did/do judge harshly the “shadow” the slightly thicker weft makes at the point of overlap, so you were supposed to put it somewhere near the edge. Or somewhere inconspicuous I guess.
Their advice was to overlap enough yarn that you could – after taking it off the loom – pull the ends through, leaving a much smaller overlap. After finishing, you then trim the ends as close to the fabric as possible. Now I’ve only tried this technique with knitting yarns, but I have to say it gives a nice result. I can imagine it working even better with finer thread.
Is this the technique you’ve used?