Hi Thread Theory!
One thing that changes dramatically as you increase speed is the effect on the thread spool and whether it is stack-wound and tall or cross-wound of any height. The greater the speed the more they wobble and jerk around, giving all-over-place tension delivery.
Make sure you have a thread felt of some sort under the spool of thread and if you have a taller stack-wound spool (a lot of modern thread spools are much taller than the old ones) try "extending" your spool pin by placing a straw over it and cutting it just a bit longer than your thread spool - or anything else that will do the same job for you.
If you have a cross-wound spool of thread they're not designed to pull off the side at all so they can wobble and jerk wickedly at higher speeds and even end up with thread wrapped around the spool pin under the thread spool resulting in top thread breaks. These are designed to pull straight up off the top of the spool (or off the end when mounted horizontally). You can get a "horizontal conversion" for cross-wound spools that sits on the normal spool pin (I got mine from The Featherweight Shop). They also have a thread stand for use in the 221 and 222 machines. I don't know if that would work in a 66 (I know the horizontal one does) but if you look I'm sure you can adapt something to work with yours that uses the same principle.
I hope that helps (and if not now, maybe for troubleshooting another day)... Megan