What kind of fabric are you trying to weld? Heat will, in most cases do exactly what you have experienced. Stitching and seam sealing is usually the most effective way of joining. I have had luck with using a product called Goop. It can be had at stores like lowe's or Home depot in the adhesives section. I wouldn't use it where stress is involved but could be used for mending a rain fly but not to build something as a eg. chair seam where weight would pull it apart. I used it to glue hook and loop onto the edge of my hammock to attach a removeable bug net. I would do a test on a small piece of fabric in question and give it the stress test to see if it will fail.
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Enjoy your next trip...