I had purchased one of those flimsy thread stands, too...
Didn't like the way it moved around...so....I went to the tool bench in the basement and found a few large metal washers. Threaded them on the spool pin and they hold the stand where I place it...and works like a dream. I even took a scrap of fabric and wrapped the washers so that I didn't have to worry about possible rust or oil problems in the future.
So...try the washers....work great.