Is the thread on a spool or a cone? I use YLI nylon monofilament on a cone (bigger than spools) and use a thread net over it. (Thread nets are often sold for serger cones.)
I also place the cone in a small glass jar behind the machine and use an "outrigger" on my machine's spool pin, which basically is just a stick with a hole in each end; one hole goes over the spool pin, and I thread the thread though the other hole. This keeps the first thread feed a little away from the machine.
For nylon thread, it's important to reduce your upper tension because nylon is stretchy. Also, when you fill the bobbin, go slowly so you do not stretch the monofilament on the bobbin. Also, especially if you have a plastic bobbin, fill the bobbin only 3/4ths full; otherwise you may be putting enough thread on the bobbin to distort the bobbin's shape.
You really do not want to use a thicker nylong thread as it will be like fishing line in the quilt! However, you may find it easier to switch to a polyester invisible thread. These are thicker than nylon monofilament but can be easier to use.