I have made thread catchers with the bag that hangs down and a pin cushion that sits on the table. For weight I use a tile and cover that. The pin cushion sits on top of the covered tile. For the pin cushion I use tightly packed fiber fill. To add more stability I put a piece of the gripper material you use under scatter rugs on the bottom of the covered tile. To hold the bag open I use stay/boning. You can buy that by the yard at most fabric stores.
My daughter-in-law made me one using a pint wide mouth mason jar. She used the ring to make a pin cushion and then made a bag that fits inside the mason jar. This is really nice for car trips when I do hand work as the jar fits in a cup holder and the jar can be used to store my scissors, thimble, needles etc. The bag is easily removed to empty threads. As an added bonus she put a picture of herself and my son on the underside of the pin cushion so when I get lonely for them all I have to do is flip it over and see two faces smiling at me. She bought some fabric to use for it because she said the fabric looked like me. Believe it or not I had some of the same fabric in my stash. She knows me well.