My biga double in size in only 3 hours (making Brinnas Pugliese page 346 in BB). Should I let it rest the remaining time, or stir down now?

For biga I would rely on time rather than volume. Stirring is probably irrelevant. The purpose of the biga is to develop flavor and establish the yeast. Usually one is concerned about volume when you are developing the structure of the dough. Structure will come later with kneading, shaping, and final rises. Then you have to be concerned with losing structure if you let the dough rise too much.

Thanks; I left it like you suggested and it turned out just fine. I was afraid it would continue to expand over the next few hours, but that didn’t happen.
Thanks again!