With my first pregnancy i was moving also and i carried a box at 28weeks up the stairs and i almost immediately lost my mucus plug. Maybe it was a coincidence.
Im 24weeks with my second and i carry a 35lb backpack around campus. And i still hold my 4yr old son sometimes and he weighs 33lbs. I haven't had any issues.
Yea your not supposed to carry anything over 20 lbs it can tear the placenta