A weft loop disappears

I think this is usually easiest to do while the piece is still on the loom. Thread a needle from the selvedge into the weave following the path of one part of the weft loop. Snip that part of the loop a little bit away from the selvedge. Thread the longer end through the eye of the needle and pull through the weave to overlap with the short end. Hold the short end with one hand if necessary so that it doesn't get pulled out through the weave. Clip both ends close to the fabric.