If i went from 199-193 in a week and a half, could this rapid weight loss result in my menstrual cycle being 6 days late?

Depends on the cause: Unlikely that the weight loss itself would cause your period to be late, though if you are restricting calories severely, or exercising a lot, both of those could cause you to be late. It’s as if your body is protecting the would-be fetus as it thinks you are in crisis, being starved. Please take a pregnancy test if late & be seen if you are having trouble maintaining a healthy lifestyle.