Weekdays – brim up
Shabbos / Yom tov (or suit occasions, like a wedding or vort) = brim down.
Wearing a brim down mid-week is a VERY yeshivish move, and would mean a whole different type of shidduch (no, I’m not kidding)
Its up there with tzitis in or our. It speaks volumes.
This is applicatble until around 45-50. Not past that yet, but I would imagine the rules are different. But for a bochur? Its VERY telling